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de Estudo de C\303\241lculo\302\251 Maplesoft, a division of Waterloo Maple Inc., 2005Cap\303\255tulo 26: Avaliando Integrais Definidas
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field>Este cap\303\255tulo poderia ser o primeiro cap\303\255tulo na Unidade 5. Est\303\241 inclu\303\255do aqui como um meio de obter pr\303\241tica adicional com a avalia\303\247\303\243o de integrais definidas (definite integrals). A principal t\303\251cnica nova que ser\303\241 introduzida \303\251 o M\303\251todo de Substitui\303\247\303\243o (Method of Substitution), uma forma integral (integral) para a Regra da Cadeia (Chain Rule).Os exemplos prov\303\252em uma variedade de diferentes problemas de integra\303\247\303\243o (integration). Os problemas gerais envolvendo integrandos representativos (representative) para integrais definidas (e indefinidas), fun\303\247\303\265es gen\303\251ricas pares (even) e \303\255mpares (odd) , e a deriva\303\247\303\243o de uma antiderivada (antiderivative) e suas propriedades para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnRjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkovJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y4 , s\303\243o discutidas em detalhes.Lembre-se que usar o maplet Integra\303\247\303\243o (Integration maplet) (o inserido no tutor Integra\303\247\303\243o Passo a Passo (Step-by-Step Integration Tutor)) para ajudar a desenvolver sua habilidade em integra\303\247\303\243o.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Gloss\303\241rio</Font></Text-field>Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio de Matem\303\241tica Maple.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Initializa\303\247\303\243o</Font></Text-field>restart;
with( plots ):
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">M\303\251todo de Substitui\303\247\303\243o </Font></Text-field>Recorde a Regra da Cadeia (Cap\303\255tulo 12): Se 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 e 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 , onde f e g s\303\243o ambas fun\303\247\303\265es diferenci\303\241veis (differentiable), ent\303\243o 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 = 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A forma integral deste resultado est\303\241 contido na seguinte afirma\303\247\303\243o(ou enunciado). 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 = 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\303\211 claro, para a integral definida, o 2\302\272 Teorema Fundamental (Fundamental Theorem) de C\303\241lculo prov\303\252 a seguinte vers\303\243o desta afirma\303\247\303\243o.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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYmRistRiM2Jy1GLDYlUSJnRidGNkY5RjwtRiM2JkZYLUYjNiQtRiw2JVEiYkYnRjZGOUZALUY9Ni1RIilGJ0ZARmVuRkVGZm5GSUZLRk1GT0Znbi9GVVEsMC4xMTExMTExZW1GJ0ZARitGQEYrRkBGaG9GQEYrRkAtRj02LVEoJm1pbnVzO0YnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yMjIyMjIyZW1GJy9GVUZhcC1GIzYnRjNGPC1GIzYmRlgtRiM2JkYrLUYjNidGXm9GPC1GIzYmRlgtRiM2JC1GLDYlUSJhRidGNkY5RkBGaG9GQEYrRkBGK0ZARmhvRkBGK0ZARitGQEYrRkA=A chave para identificar o integrando (integrand) como um produto (product) de uma express\303\243o que envolve LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtRiM2Ji1GOzYtUSIoRidGPi9GQUY2RkMvRkZGNkZHRklGS0ZNL0ZQUSwwLjE2NjY2NjdlbUYnL0ZTRmZuLUYjNiQtRiw2JVEieEYnRjRGN0Y+LUY7Ni1RIilGJ0Y+RllGQ0ZaRkdGSUZLRk1GZW4vRlNRLDAuMTExMTExMWVtRidGPkYrRj5GK0Y+ e a derivada (derivative)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. Na pr\303\241tica, geralmente se reescreve o integrando usando a substitui\303\247\303\243o 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 e trocando o diferencial 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 por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn, obtendo deste 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Isto coloca a integral na forma 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 = 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 qual \303\251 f\303\241cil identificar uma antiderivada. Tudo o que resta \303\251 usar a substitui\303\247\303\243o para reescrever a antiderivada em termos da vari\303\241vel independente original, 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 = 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 os mesmos passos s\303\243o repetidos para uma integral definida o m\303\251todo pode ser escrito 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 = 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
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 26.1: Integral Indefinida </Text-field>Avaliar a integral indefinida 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 que, no integrando, o numerador (numerator)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= \303\251 derivada de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUklbXN1cEdGJDYlLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtbkdGJDYkUSIyRicvRjtRJ25vcm1hbEYnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRkFGK0ZB. E como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUklbXN1cEdGJDYlLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtbkdGJDYkUSIyRicvRjtRJ25vcm1hbEYnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRkFGK0ZB aparece em outra parte no integrando, esta observa\303\247\303\243o n\303\243o \303\251 imediatamente \303\272til como uma antiderivada de 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 , n\303\243o \303\251 imediatamente conhecida. Mas, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= \303\251 tamb\303\251m a derivada de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIrRidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZNLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnLUYyNiRRIjJGJ0Y1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjVGK0Y1RitGNQ== e uma antiderivada de 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 \303\251 conhecida. De fato, isto \303\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Para juntar isto para completar a avalia\303\247\303\243o desta integral indefinida pelo M\303\251todo da Substitui\303\247\303\243o, fazemos 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 e assim 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 e
Como a derivada da antiderivada geral \303\251 o integrando original, a computa\303\247\303\243o foi feita corretamente.
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Solu\303\247\303\243o usando o maplet </Font><Font italic="true">Integration</Font><Font encoding="UTF-8"> (Integra\303\247\303\243o)</Font></Text-field>O Integration maplet ( maplet Integra\303\247\303\243o) pode ser usado para ajudar a encontrar a antiderivada neste problema. Veja a Figura 26.1.The Integration maplet can be used to help find the antiderivative in this problem. See Figure 26.1.Entre com o integrando (Enter a function)bot\303\243o Inicialize (Start) \342\207\222AM\303\272ltiplo de Constante (Constant Multiple)\342\207\222BMudar (Change)\342\207\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M\303\272ltiplo de Constante (Constant Multiple)\342\207\222DPot\303\252ncia (Power)\342\207\222EReverter (Revert) \342\207\222F
A substitui\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdXBHRiQ2JS1GLDYlUSJ4RidGL0YyLUkjbW5HRiQ2JFEiMkYnRjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYsNiNRIUYnRjk= resulta na nova integral 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, n\303\243o um integrando para o qual conhecemos correntemente uma antiderivada.
<Text-field style="Heading 3" layout="Heading 3">Nota</Text-field>Se for pedido ao maplet Integra\303\247\303\243o (Integration maplet) para mostrar Todos os Passos (All Steps) na avalia\303\247\303\243o desta integral os resultados ser\303\243o diferentes do ---mas no final eq\303\274ivalente a --- que \303\251 mostrado na Figura 26.1. A diferen\303\247a \303\251 que depois de D, o Maplet faz outra troca de vari\303\241veis em vez de usar a Regra de Pot\303\252ncia.
<Text-field style="Heading 1" readonly="true" layout="Heading 1"><Font readonly="true">Maple T.A. Maple-Graded Question</Font></Text-field>Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.
<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional.
In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.with(RandomTools):
randomize():
nn1 := Generate(integer(range=2..3)):
nn2 := Generate(integer(range=1..10)):
nn3 := Generate(choose([2,3,4,5])):
nn4 := Generate(rational(range=0..1,denominator=nn3)):
ff1 := sort(Generate(polynom(integer(range=1..10),x,degree=nn1)),x):
ff2 := diff(ff1,x) * Generate(choose([-nn2,nn2])):
fn1 := Int(ff2/ff1^nn4,x);
ans1 := value(fn1) + C;JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 26.1</Font></Text-field>The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component.
In the following text region, enter the full contents of the question.Avaliar a integral indefinida `$fn1`JSFH
<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.JSFHans1;JSFH
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0);
Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.evalb(`$ANSWER`-`$RESPONSE`=0);
<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional.
Enter your hints in the following table. You can provide up to three hints.
Is the derivative of `$ff1` in the function?Try to factor out the derivative of `$ff1`.Don't forget the constant after finding the antiderivative.
with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Is the derivative of</mtext><mtext> </mtext><mtext></mtext><mrow><mrow><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>6</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>7</mn></mrow></mrow><mtext></mtext><mtext> in the function?</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet); with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Try to factor out the derivative of </mtext><mtext></mtext><mrow><mrow><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>6</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>7</mn></mrow></mrow><mtext></mtext><mtext>.</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet); with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Don't forget the constant after finding the antiderivative.</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);
<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.Replace this text with feedback.with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea0`, `value`); ANSWER := ans1; if evalb(ANSWER-eval(parse(StudentResponse))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!
</mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>
</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>27</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mfenced open='(' close=')' separators=','><mrow><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>6</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>7</mn></mrow></mfenced><mrow><mn>1</mn><mo lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&sol;</mo><mn>3</mn></mrow></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>
</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>27</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mfenced open='(' close=')' separators=','><mrow><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>6</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>7</mn></mrow></mfenced><mrow><mn>1</mn><mo lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&sol;</mo><mn>3</mn></mrow></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 26.2: Integral Definida </Text-field>Avaliar a integral definidaLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2LEYrLUkobXN1YnN1cEdGJDYnLUkjbW9HRiQ2LVEmJmludDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTS1GIzYmLUY1Ni1RKCZtaW51cztGJ0Y4RjtGPi9GQUY9RkMvRkZGPUZHRklGS0ZOLUkmbWZyYWNHRiQ2KC1GLDYlUSUmcGk7RicvJSdpdGFsaWNHRj1GOC1JI21uR0YkNiRRIjZGJ0Y4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Ziby8lKWJldmVsbGVkR0Y9RitGOC1GIzYmRistRlg2KEZaLUZqbjYkUSIzRidGOEZdb0Zgb0Zjb0Zlb0YrRjgvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRmBwRistRiM2Ji1GLDYlUSRjb3NGJy9GaG5GQi9GOVEnaXRhbGljRictRjU2LVEwJkFwcGx5RnVuY3Rpb247RidGOEY7Rj5GVUZDRlZGR0ZJRktGTi1JKG1mZW5jZWRHRiQ2JC1GIzYmRltwLUY1Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y4RjtGPkZVRkNGVkZHRklGS0ZOLUYsNiVRKCZ0aGV0YTtGJ0ZnbkY4RjhGOEY4RistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuM2VtRicvJSZkZXB0aEdGXnIvJSpsaW5lYnJlYWtHUSVhdXRvRidGKy1GIzYmLUY1Ni1RMCZEaWZmZXJlbnRpYWxEO0YnRjhGO0Y+RlVGQ0ZWRkdGSUZLRk5GZnFGOC9JK21zZW1hbnRpY3NHRiRRImRGJ0YrRjhGK0Y4para a qual Maple d\303\241 imediatamenteq := Int(cos(3*theta), theta=-Pi/6..Pi/3):
q = value(q);A \303\272nica forma da fun\303\247\303\243o cosseno (cosinefunction) que tem uma antiderivada conhecida \303\251 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 de 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proceda da seguinte forma.
Para colocar uma integral dada em uma forma que possa ser usada, escreva 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 e assim 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 . De fato, os c\303\241lculos devem come\303\247ar comLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjNGJ0Y5LUYsNiVRKCZ0aGV0YTtGJy9GMEY9RjlGOQ==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 \342\207\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\303\243o, a troca das vari\303\241veis LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjNGJ0Y5LUYsNiVRKCZ0aGV0YTtGJy9GMEY9RjlGOQ== pode ser implementada na integral definida para obter
<Text-field style="Heading 1" readonly="true" layout="Heading 1"><Font readonly="true">Maple T.A. Maple-Graded Question</Font></Text-field>Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.
<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional.
In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.with(RandomTools):
randomize():
nn5 := Generate(integer(range=2..3)):
nn6 := Generate(integer(range=1..10)):
nn7 := Generate(choose([2,3,4,5])):
nn8 := Generate(rational(range=0..1,denominator=nn7)):
nn9 := Generate(integer(range=0..9)):
nn10 := Generate(integer(range=1..10)):
while (nn9 >= nn10) do nn10 := Generate(integer(range=-10..10)) end do:
nn11 := Generate(choose([2,3,4,6])):
nn12 := Generate(rational(range=0..1,denominator=nn11)):
nn13 := Generate(rational(range=0..2,denominator=nn11)):
while (nn12 >= nn13) do
nn13 := Generate(rational(range=0..2,denominator=nn11)):
end do:
nn12 := Pi*nn12:
nn13 := Pi*nn13:
ff3 := sort(Generate(polynom(integer(range=1..10),x,degree=nn5)),x):
ff4 := diff(ff3,x) * Generate(choose([-nn6,nn6])):
ff5 := Generate(choose([cos(nn7*x),sin(nn7*x)])):
ff6 := diff(ff5,x):
fn2_[1] := Int(ff4/ff3^nn8,x=nn9..nn10):
ans2_[1] := evalf(value(fn2_[1])):
fn2_[2] := Int(ff5,x=nn12..nn13):
ans2_[2] := value(fn2_[2]):
fn2_[3] := Int(ff5*ff6,x=nn12..nn13):
ans2_[3] := value(fn2_[3]):
nn14 := Generate(choose([1,2,3])):
fn2 := fn2_[nn14];
ans2 := ans2_[nn14];JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 26.2</Font></Text-field>The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component.
In the following text region, enter the full contents of the question.Avalie a integral definida `$fn2`.
D\303\252 uma resposta exata, ou, uma aproxima\303\247\303\243o com precis\303\243o de at\303\251 5 d\303\255gitos significativos.
JSFH
<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.ans2;JSFH
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0);
Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.evalb( fnormal(evalf(`$ANSWER`-`$RESPONSE`), 5 ) = 0 );
<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional.
Enter your hints in the following table. You can provide up to three hints.
Can a substitution be made?Does a second substitution need to be made?Replace this text with hint 3.
with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Can a substitution be made?</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet); with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext></mtext><mtext> </mtext><mtext>Does a second substitution need to be made?</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);
<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.Replace this text with feedback.with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea1`, `value`); ANSWER := ans2; if evalb( fnormal(evalf(ANSWER-eval(parse(StudentResponse))), 5 ) = 0 ) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!
</mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>
</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>19.25548344</mn></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>
</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>19.25548344</mn></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Exemplo 26.3: Fun\303\247\303\243o \303\215mpar em um intervalo Sim\303\251trico </Font></Text-field>Recorde que uma fun\303\247\303\243o \303\255mpar (odd ) \303\251 uma fun\303\247\303\243o com a propriedade: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYmRistRiM2JS1GPTYtUSomdW1pbnVzMDtGJ0ZARkJGRUZHRklGS0ZNRk9GUUZULUYsNiVRInhGJ0Y2RjlGQEYrRkAtRj02LVEiKUYnRkBGZW5GRUZmbkZJRktGTUZPRmduL0ZVUSwwLjExMTExMTFlbUYnRkBGK0ZALUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGXXAtRiM2JkZeby1GIzYnRjNGPC1GIzYmRlgtRiM2JEZhb0ZARmRvRkBGK0ZARitGQEYrRkBGK0ZA . Uma fun\303\247\303\243o \303\255mpar \303\251 chamada sim\303\251trica em rela\303\247\303\243o \303\240 origem. Quando uma fun\303\247\303\243o \303\255mpar \303\251 integrada sobre um intervalo sim\303\251trico(symmetricinterval)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYnRistRiM2JS1GMjYtUSomdW1pbnVzMDtGJ0Y1L0Y5Rj1GOy9GP0Y9RkBGQkZERkYvRklRJjAuMGVtRicvRkxGVy1GLDYlUSJhRicvJSdpdGFsaWNHRjovRjZRJ2l0YWxpY0YnRjUtRjI2LVEiLEYnRjVGVC9GPEY6RlVGQEZCRkRGRkZWL0ZMUSwwLjMzMzMzMzNlbUYnRllGNS1GMjYtUSJdRidGNUY4RjtGPkZARkJGREZGRkgvRkxRLDAuMTExMTExMWVtRidGNUYrRjU= onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYsNiVRJGA+YEYnRjRGN0Y6LUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=, o valor (value) da integral pode ser simplificada. Suponha que 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 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYsNiVRJGA+YEYnRjRGN0Y6LUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=. Ent\303\243o, pela simetria, a "\303\241rea" sobre a curva (curve) no intervalo 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 \303\251 o negativo (negative) da \303\241rea sob a curva no intervalo 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.Isto est\303\241 ilustrado na Figura 26.2.
Figura 26.2 O "cancelamento" das \303\241reas de uma fun\303\247\303\243o \303\255mpar em um intervalo sim\303\251trico
No gr\303\241fico (graph) acima note como a \303\241rea rosa positiva (positive) cancela exatamente a \303\241rea azul negativa. Isto sugere que 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 provar que qualquer fun\303\247\303\243o \303\255mpar (integr\303\241vel), separe o intervalo original 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 em duas regi\303\265es, 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 e 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. para a integral em 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 use a substitui\303\247\303\243o 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 . Logo 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, 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, e a integral resultante \303\251
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(Substitui\303\247\303\243o)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUYjNistRiw2LVEoJm1pbnVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSShtc3Vic3VwR0YkNictRiw2LVEmJmludDtGJ0YvRjJGNS9GOFEldHJ1ZUYnRjkvRjxGUkY9Rj8vRkJRJjAuMGVtRicvRkVGVS1JI21pR0YkNiVRImFGJy8lJ2l0YWxpY0dGUi9GMFEnaXRhbGljRictSSNtbkdGJDYkUSIwRidGLy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJS9zdWJzY3JpcHRzaGlmdEdGX28tRlg2I1EhRictRiM2Ji1GWDYlUSJmRidGZW5GZ24tRiw2LVEwJkFwcGx5RnVuY3Rpb247RidGL0YyRjVGN0Y5RjtGPUY/RlRGVi1JKG1mZW5jZWRHRiQ2JC1GIzYkLUZYNiVRKyZ1bWludXMwO3VGJ0ZlbkZnbkYvRi9GLy1GLDYtUTEmSW52aXNpYmxlVGltZXM7RidGL0YyRjVGN0Y5RjtGPUY/RlRGVi1GWDYlUSNkdUYnRmVuRmduLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjNlbUYnLyUmZGVwdGhHRmBxLyUqbGluZWJyZWFrR1ElYXV0b0YnRmJvRi9GYm9GLw==(Regra de Multiplica\303\247\303\243o por Constante)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(Defini\303\247\303\243o de Fun\303\247\303\243o \303\215mpar)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(Regra de Multiplica\303\247\303\243o por Constante)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(Propriedade de Integral Definida)
Ent\303\243o, relembrando que a vari\303\241vel da integra\303\247\303\243o em uma integral definida n\303\243o afeta o valor da integral, escreva
Um exemplo de como isto pode ser usado para avaliar uma integral definida de uma fun\303\247\303\243o \303\255mpar sobre um intervalo n\303\243o sim\303\251trico, a seguir: Para avaliar 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-se deduzir que o integrando \303\251 uma fun\303\247\303\243o \303\255mpar para reduzir o problema a uma integra\303\247\303\243o sobre um intervalo menor. Os c\303\241lculos s\303\243o resumidos abaixo.
Esta computa\303\247\303\243o \303\251 um pouco mais simples pois que n\303\243o precisa manipular todos os sinais negativos que poderiam aparecer de um limite mais baixo de 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 .
<Text-field style="Heading 1" readonly="true" layout="Heading 1"><Font readonly="true">Maple T.A. Maple-Graded Question</Font></Text-field>Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.
<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional.
In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.with(RandomTools):
with(plots):
randomize():
n1 := Generate(integer(range=-10..10)):
n2 := Generate(integer(range=-10..10)):
while (n1=n2) do
n2 := Generate(integer(range=-10..10)):
end do:
r1 := Generate(choose([-10..-1,1..10])):
n3 := Generate(integer(range=r1)):
n4 := Generate(choose([1,3,5])):
n5 := Generate(choose([Pi,2,3,4,5,6,7,8,9,10])):
ff8 := n1*x^n4+n2*sin(n3*x):
ff9 := n1*x^n4+n2*sin(x)+n3:
fn3 := Generate(choose([ff8,ff9]));
ans3 := Int(fn3,x=-n5..n5);
value(ans3);
dispfn3 := Int(f(x),x=-n5..n5);
JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 26.3</Font></Text-field>The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component.
In the following text region, enter the full contents of the question.Dado f(x) = `$fn3`, qual \303\251 o valor da integral definida `$dispfn3`?
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JSFH
<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.JSFHeval(value(ans3),Pi=`π`);
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0);
Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.evalb(evalf(value(`$ans3`)-`$RESPONSE`,5)=0);
<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional.
Enter your hints in the following table. You can provide up to three hints.
Is the function odd?Replace this text with hint 2.Replace this text with hint 3.
with(StringTools): with(DocumentTools): response := GetProperty(`TextArea3`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Is the function odd?</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);
<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.Replace this text with feedback.with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea3`, `value`); ANSWER := eval(value(ans3),Pi=`π`); if evalb(evalf(value(ans3)-eval(parse(StudentResponse)),5)=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!
</mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>
</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>0</mn></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>
</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>0</mn></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Exemplo 26.4: Fun\303\247\303\243o Par em um intervalo </Font><Hyperlink linktarget="Dictionary:Definition,symmetric" hyperlink="true"><Font style="Heading 1" encoding="UTF-8">Sim\303\251trico</Font></Hyperlink></Text-field>Relembre que uma fun\303\247\303\243o par (even) \303\251 uma fun\303\247\303\243o com a propriedade de que 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. Uma fun\303\247\303\243o par \303\251 chamada de sim\303\251trica em rela\303\247\303\243o ao eixo- LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. quando uma fun\303\247\303\243o par \303\251 integrada sobre um intervalo sim\303\251trico 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 onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYsNiVRJGA+YEYnRjRGN0Y6LUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=, o valor da integral pode ser simplificado. Suponha que 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 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYsNiVRJGA+YEYnRjRGN0Y6LUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=. Ent\303\243o, pela simetria, a "\303\241rea" sob a curva no intervalo 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 \303\251 a mesma que a \303\241rea sob a curva no intervalo 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.A Figura 26.3 ilustra esta id\303\251ia.
Figura 26.3 As \303\241reas iguais (matching) no gr\303\241fico de uma fun\303\247\303\243o par em um intervalo sim\303\251trico
No gr\303\241fico acima, note como a \303\241rea rosa positiva se equipara exatamente a \303\241rea azul negativa. Isto sugere 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Para provar isto para qualquer fun\303\247\303\243o par (integr\303\241vel), separe o intervalo original 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 em duas regi\303\265es, 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 e 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. Para a integral em 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, use a substitui\303\247\303\243o 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 tal que 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, 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, a integral resultante \303\251:
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(Substitui\303\247\303\243o)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(Regra de Multiplica\303\247\303\243o por Constante)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(Definition de Fun\303\247\303\243o Par)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(Propriedade de Integral Definida)
E , relembrando que a vari\303\241vel de integra\303\247\303\243o em uma integral definida n\303\243o afeta o valor da integral, tem-se
<Text-field style="Heading 1" readonly="true" layout="Heading 1"><Font readonly="true">Maple T.A. Maple-Graded Question</Font></Text-field>Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.
<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional.
In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.with(plots):
with(RandomTools):
randomize():
n6 := Generate(integer(range=-10..10)):
n7 := Generate(integer(range=1..5))*2:
while (n6=n7) do
n7 := Generate(integer(range=1..5))*2:
end do:
r2 := Generate(choose([-10..-1,1..10])):
n8 := Generate(integer(range=r2)):
n9 := Generate(choose([1,3,5])):
n10 := Generate(choose([Pi,2,3,4,5,6,7,8,9,10])):
n11 := Generate(integer(range=2..5)):
ff10 := n6*x^n7*cos(n8*x):
ff11 := n6*x^(n7/2)*cos(x)+n9:
ff12 := abs(sort(Generate(polynom(integer(range=-10..10),x,degree=n11)))):
ff13 := abs(sort(Generate(polynom(integer(range=-10..10),x,degree=n11)))) + n11:
fn4 := Generate(choose([ff10,ff11,ff12,ff13]));
if (evalf(eval(fn4,x=5))=evalf(eval(fn4,x=-5))) then
ans4 := 2*Int(fn4,x=0..n10);
else
ans4 := Int(fn4,x=-n10..n10);
end if;
value(ans4);
dispfn4 := Int(f(x),x=-n10..n10);
#plot(fn4,x=-n10..n10);
JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 26.4</Font></Text-field>The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component.
In the following text region, enter the full contents of the question.Dado f(x) = `$fn4`, qual \303\251 o valor da integral definida `$dispfn4`?
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JSFH
<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.evalf(value(ans4));JSFH
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0);
Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.evalb(evalf(value(`$ans4`)-`$RESPONSE`,6)=0);
<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional.
Enter your hints in the following table. You can provide up to three hints.
Is the function even?Replace this text with hint 2.Replace this text with hint 3.
with(StringTools): with(DocumentTools): response := GetProperty(`TextArea4`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Is the function even?</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);
<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.`$ans4` = `$ANSWER`with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea4`, `value`); ANSWER := evalf(value(ans4)); ; if evalb(evalf(value(ans4)-eval(parse(StudentResponse)),6)=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!
</mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>
</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>6.283185308</mn></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext></mtext><mrow><mrow><msubsup superscriptshift='2'><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&int;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mi mathvariant='normal'>&pi;</mi></mrow><mi mathvariant='normal'>&pi;</mi></msubsup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><mi mathvariant='normal'>cos</mi><mo lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></mfenced><mspace height='0.0ex' width='0.3em' depth='0.0ex' linebreak='auto'/><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>ⅆ</mo><mi>x</mi></mrow></mrow><mtext></mtext><mtext> = </mtext><mrow><mn>6.283185308</mn></mrow><mtext></mtext><mtext>
</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>6.283185308</mn></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 26.5: <Hyperlink linktarget="Dictionary:Definition,indefiniteintegral" hyperlink="true"><Font style="Heading 1">Antiderivada para</Font></Hyperlink> <Equation executable="false" style="2D Math_42" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiUtSSNtbkdGJDYlUSIxRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjpGOEY7LUYjNiUtRiw2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y5USxib2xkLWl0YWxpY0YnRjtGOEY7LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZMLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOEY7">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiUtSSNtbkdGJDYlUSIxRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjpGOEY7LUYjNiUtRiw2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y5USxib2xkLWl0YWxpY0YnRjtGOEY7LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZMLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOEY7</Equation><Equation executable="false" style="Heading 1" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDL0YwUSVib2xkRicvJStmb250d2VpZ2h0R0ZH">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDL0YwUSVib2xkRicvJStmb250d2VpZ2h0R0ZH</Equation></Text-field>Relembre que existe uma pot\303\252ncia (power) para a qual n\303\243o conhecemos uma antiderivada, a saber,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 , para todo 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, como 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 \303\251 cont\303\255nua (continuous) para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYsNiVRJGA+YEYnRjRGN0Y6LUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=, sabemos que esta fun\303\247\303\243o \303\251 Riemann integr\303\241vel (Riemann integrable) em 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. O Primeiro Teorema Fundamental de C\303\241lculo garante que a antiderivada existe e pode ser escrita em termos de uma integral definida. Portanto, escrevemos f5 := 1/t:
F5 := Int( f5, t=1..x ):
L(x) = F5;Vamos mostrar algumas propriedades desta antiderivada
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Propriedade 1: <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUkjbW5HRiQ2JFEiMUYnRkBGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZpby1GXW82JFEiMEYnRkBGQEYrRkA=">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</Equation> </Text-field>As propriedes para Integrais Definidas nos diz imediatamente um valor-de-fun\303\247\303\243o para esta fun\303\247\303\243o, a saber,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 = 0
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Propriedade 2: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> </Text-field>Esta propriedade requer o uso do M\303\251todo de Substitui\303\247\303\243o com 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 . Assim 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 , 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, e os limites de integra\303\247\303\243o s\303\243o convertidos 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 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= e 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 to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInhGJ0Y0RjdGPkYrRj4=. Portanto, escrevemos
A remanescente integral definida, n\303\243o identificada, pode ser simplificada com a substitui\303\247\303\243o 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 . Assim 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, 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, e os limites de integra\303\247\303\243o s\303\243o convertidos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInhGJ0Y0RjdGPkYrRj4= para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= e de 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 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInlGJ0Y0RjdGPkYrRj4=. Quando juntamos todos estes resultados, encontramos
Portanto, para todos os valores positivos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn, 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
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Propriedade 4: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> </Text-field>As propriedades 3 e 2 combinam resultandoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYmRistSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEieEYnRjZGOUZALUYjNiQtRiw2JVEieUYnRjZGOUZALyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZecC8lKWJldmVsbGVkR0ZERitGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZccS1GIzYnRjNGPC1GIzYmRlgtRiM2JkYrLUYjNidGYW8tRj02LVExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlQtRl1vNigtRiM2JC1JI21uR0YkNiRRIjFGJ0ZARkBGZG9GaW9GXHBGX3BGYXBGK0ZARitGQEZjcEZARitGQEYrRkBGK0ZA = 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 propriedades s\303\243o reminiscentes das propriedades da fun\303\247\303\243o logar\303\255tmica (natural). Para justificar posteriormente esta associa\303\247\303\243o, observe que a fun\303\247\303\243o L \303\251 crescente (increasing) para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYsNiVRJGA+YEYnRjRGN0Y6LUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= porque LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEjTCdGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUy1GIzYmLUY9Ni1RIihGJ0ZAL0ZDRjhGRS9GSEY4RklGS0ZNRk8vRlJRLDAuMTY2NjY2N2VtRicvRlVGaG4tRiM2JC1GLDYlUSJ4RidGNkY5RkAtRj02LVEiKUYnRkBGZW5GRUZmbkZJRktGTUZPRmduL0ZVUSwwLjExMTExMTFlbUYnRkBGK0ZALUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGaG8tSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRidGQEZARmpuLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZocC8lKWJldmVsbGVkR0ZERitGQEYrRkA= > 0. Em particular, 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 para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYsNiVRJGA+YEYnRjRGN0Y6LUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= e 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 para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSI8RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZNLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkjbW9HRiQ2LVEiPEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUkjbW5HRiQ2JFEiMUYnRjVGNUYrRjU=. Como L n\303\243o tem pontos cr\303\255ticos, o gr\303\241fico \303\251 sempre c\303\264ncavo bara baixo (concave down) porque LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEkTCcnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlMtRiM2Ji1GPTYtUSIoRidGQC9GQ0Y4RkUvRkhGOEZJRktGTUZPL0ZSUSwwLjE2NjY2NjdlbUYnL0ZVRmhuLUYjNiQtRiw2JVEieEYnRjZGOUZALUY9Ni1RIilGJ0ZARmVuRkVGZm5GSUZLRk1GT0Znbi9GVVEsMC4xMTExMTExZW1GJ0ZARitGQC1GPTYtUSI9RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjI3Nzc3NzhlbUYnL0ZVRmhvLUYjNiYtRj02LVEqJnVtaW51czA7RidGQEZCRkVGR0ZJRktGTUZPRlFGVC1JJm1mcmFjR0YkNigtRiM2JC1JI21uR0YkNiRRIjFGJ0ZARkAtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JUZcby1GZXA2JFEiMkYnRkAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGQEYrRkAvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmpxLyUpYmV2ZWxsZWRHRkRGK0ZARitGQEYrRkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkjbW9HRiQ2LVEiPEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUkjbW5HRiQ2JFEiMEYnRjVGNUYrRjU=. Todas estas caracter\303\255sticas est\303\243o apresentadas na Figura 26.4, um gr\303\241fico de L.
Todas estas propriedades e o gr\303\241fico acima nos leva a concluir que 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, o logar\303\255tmo natural.
<Text-field style="Heading 1" readonly="true" layout="Heading 1"><Font readonly="true">Maple T.A. Maple-Graded Question</Font></Text-field>Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.
<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional.
In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.with(RandomTools):
randomize():
rr5 := Generate(choose([-10..-1,1..10])):
ff7 := 1/(Generate(integer(range=rr5))*x+Generate(integer(range=-10..10)));
fn5 := Int(ff7,x);JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 26.5</Font></Text-field>The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component.
In the following text region, enter the full contents of the question.Avaliar `$fn5`
(Note: deve-se entrar com a resposta antes de clicar "Grade".)JSFH
<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.JSFHvalue(fn5)+C;JSFH
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0);
Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.evalb(simplify(`$ANSWER`-`$RESPONSE`)=0);
<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional.
Enter your hints in the following table. You can provide up to three hints.
Don't forget the constant after finding the antiderivative.Replace this text with hint 2.Replace this text with hint 3.
with(StringTools): with(DocumentTools): response := GetProperty(`TextArea2`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Don't forget the constant after finding the antiderivative.</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);
<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.Replace this text with feedback.with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea2`, `value`); ANSWER := value(fn5)+C; if evalb(simplify(ANSWER-eval(parse(StudentResponse)))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!
</mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>
</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><mrow><mi mathvariant='normal'>ln</mi><mo lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>10</mn></mrow></mrow></mfenced></mrow></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>
</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><mrow><mi mathvariant='normal'>ln</mi><mo lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>10</mn></mrow></mrow></mfenced></mrow></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Sum\303\241rio</Font></Text-field>O M\303\251todo de Substitui\303\247\303\243o \303\251 uma das t\303\251cnicas de integra\303\247\303\243o consideradas neste curso. Este m\303\251todo prov\303\252 uma vers\303\243o de antiderivada da Regra da Cadeia para deriva\303\247\303\243o. Este m\303\251todo expande bastante a classe de integrais que podem ser computadas explicitamente (explicitly). M\303\251todos adicionais, particularmente uma antiderivada an\303\241loga a da Regra do Produto, ser\303\243o desenvolvidos no pr\303\263ximo curso na seq\303\274\303\252ncia de c\303\241lculo.Enquanto que o logar\303\255tmo natural n\303\243o \303\251 geralmente discutido neste curso, o M\303\251todo de Substitui\303\247\303\243o e as id\303\251ias no Cap\303\255tulo 18 sobre constru\303\247\303\243o de gr\303\241fico (Graphing) sugere fortemente que o logar\303\255tmo natural \303\251 uma antiderivada para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnRjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkovJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y4 , de modo 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
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Qual \303\251 o Pr\303\263ximo?</Font></Text-field>Agora que terminou este cap\303\255tulo, voc\303\252 deve afiar a sua capacidade em integra\303\247\303\243o (e antideriva\303\247\303\243o) com tarefas online. O Integration maplet ( maplet Integra\303\247\303\243o)(inserido no Step-by-Step Integration Tutor) pode ser muito \303\272til quando explorar como diferentes substitui\303\247\303\265es muda uma integral. A \303\272ltima unidade neste curso apresenta um a cole\303\247\303\243o de aplica\303\247\303\265es da integral. Chapter Navigation<< Prev12345678910111213141516171819202122232425 26 2728293031Next >>
Table of Contents\302\251 Maplesoft, a division of Waterloo Maple Inc., 2005. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
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