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de Estudo de C\303\241lculo\302\251 Maplesoft, a division of Waterloo Maple Inc., 2005Cap\303\255tulo 27: \303\201rea de uma Regi\303\243o Plana
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field>A \303\241rea \303\251 usada no Cap\303\255tulo 23 para iniciar o desenvolvimento de integral definida (definite integral). Naquele contexto todas as \303\241reas s\303\243o computadas como limites expl\303\255citos (explicitlimits). Os Teoremas Fundamentais de C\303\241lculo prov\303\252m ferramentas eficientes para avaliar uma integral definida. A id\303\251ia essencial desenvolvida neste cap\303\255tulo \303\251 resumida como fatiar (slice), aproximar, limitar, avaliar (evaluate). O processo geral usado para expressar a \303\241rea (area) de uma regi\303\243o plana como uma integral definida consiste nos passos: dividir em fatias, aproximar e limitar (limit). Uma vez formulada a integral definida apropriada, o passo final de avaliar (evaluate) pode ser implementado. Este mesmo processo \303\251 usado em outras aplica\303\247\303\265es consideradas nesta unidade, assim como muitas outras aplica\303\247\303\265es de integral definida fora do alcance desta unidade.
<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 (Maple Math Dictionary).
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Inicializa\303\247\303\243o</Font></Text-field>restart;with( plots ):
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Exemplo 27.1: Regi\303\243o Entre Duas Curvas </Font></Text-field>A regi\303\243o limitada pelos pelos gr\303\241ficos (graphs) de top1 := sqrt(x):
y = top1;ebot1 := x^2:
y = bot1;no intervalo (interval)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 \303\251 mostrada na Figura 27.1.
plot([top1,bot1], x=0..1, color=[red,blue]);
Figura 27.1 Exemplo 27.1: Gr\303\241ficos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic= (vermelho) e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GOVEnbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGPw== (azul)
A \303\241rea desta regi\303\243o \303\251 dada pela integral definida A1 := Int( top1-bot1, x=0..1 ):
Area = A1;Cujo valor (value) \303\251A1 = value( A1 );
<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():
aa1 := Generate(integer(range=1..3)):
cc1 := Generate(integer(range=-5..-1)):
fn1 := aa1*x^2+cc1;
aa2 := Generate(integer(range=-3..3)):
while (aa2 >= aa1) do aa2 := Generate(integer(range=-3..3)) od:
bb2 := Generate(integer(range=-3..3)):
while (4*(aa1-aa2)*cc1 >= bb2^2 ) do bb2 := Generate(integer(range=-3..3)) od:
fn2 := aa2*x^2+bb2*x;
lo := (bb2-sqrt(bb2^2-4*(aa1-aa2)*cc1))/2/(aa1-aa2);
hi := (bb2+sqrt(bb2^2-4*(aa1-aa2)*cc1))/2/(aa1-aa2);
ans1 := Int(sort(fn2-fn1,x),x=lo..hi);
#DocumentTools[SetProperty]( Plot0, value, plot([fn1,fn2],x=lo-1..hi+1) );JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 27.1</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.Qual \303\251 a \303\241rea da regi\303\243o entre y = `$fn1` (vermelho) e y = `$fn2` (verde)?
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
<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 `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.JSFHevalf(value(ans1));JSFH
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$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.
Find the points of intersection for the interval of the definite integral.Replace this text with hint 2.Replace this text with hint 3.
with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Find the points of intersection for the interval of the definite integral.</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 `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.The definite integral is `$ans1` = `$ANSWER`with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea0`, `value`); ANSWER := evalf(value(ans1)); 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>1.041131863</mn></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>The definite integral is </mtext><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><mfrac><mn>3</mn><mn>10</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mfrac><mn>1</mn><mn>10</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>29</mn></msqrt></mrow></mrow></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mn>3</mn><mn>10</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mn>10</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>29</mn></msqrt></mrow></mrow></mrow></msubsup><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>5</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'>−</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></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>1.041131863</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>1.041131863</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 27.2: \303\201rea Positiva e \303\201rea Negativa </Font><Hyperlink linktarget="Dictionary:Definition,positive" hyperlink="true"><Font style="Heading 1"> </Font></Hyperlink></Text-field>A \303\241rea entre os gr\303\241ficos def2 := sqrt(x):
y = f2;eg2 := exp(-3*x):
y = g2;no intervalo (interval)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 consiste de duas partes porque as curvas se cruzam uma com a outra. As curvas e a \303\241rea fechada s\303\243o mostradas na Figura 27.
Figura 27.2 Exemplo 27.2: Gr\303\241ficos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic= (vermelho), 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 (azul), e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk= (verde)
A primeira parte da \303\241rea tem a curva (curve) exponencial no contorno superior e a raiz (root) quadrada como contorno inferior; depois que as curvas se interceptam, estes papeis s\303\243o revertidos. Figura 27.3 enfatiza isto.
Figura 27.3A curva por partes amarela permanece em cima; a azul, em baixo
A \303\241rea fechada total \303\251 a soma de duas integrais definidas, a saber,A1 := Int( g2-f2, x=0..T ):
A2 := Int( f2-g2, x=T..1 ):
Area = A1 + A2;onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 a coordenada-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= do ponto onde as duas curvas se intersecionam. O valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 T_exact := solve( f2=g2, x ):
T_approx := evalf( T_exact ):
T = T_exact;
`` = T_approx;assim, a \303\241rea requerida \303\251Area = A1 + A2;
`` = value( eval( A1 + A2, T=T_approx ) );
<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():
aa3 := Generate(integer(range=2..5)):
cc2 := Generate(integer(range=-5..-1)):
fn3 := aa3*x^2+cc2;
aa4 := Generate(integer(range=-4..4)):
while (aa4 >= aa3) do aa4 := Generate(integer(range=-4..4)) end do:
bb4 := Generate(integer(range=-3..3)):
while (4*(aa3-aa4)*cc2 >= bb4^2 ) do bb4 := Generate(integer(range=-3..3)) end do:
fn4 := aa4*x^2+bb4*x;
clow := (bb4-sqrt(bb4^2-4*(aa3-aa4)*cc2))/2/(aa3-aa4);
chigh := (bb4+sqrt(bb4^2-4*(aa3-aa4)*cc2))/2/(aa3-aa4);
nn1 := Generate(integer(range=-5..3)):
nn2 := Generate(integer(range=-2..5)):
while (nn2 <= nn1) do nn2 := Generate(integer(range=-2..4)) end do:
if ((evalf(clow)<evalf(nn1) and (evalf(chigh)<evalf(nn1) or evalf(chigh)>evalf(nn2))) or evalf(clow>evalf(nn2))) then
# only nn1 and nn2 matter
temp1 := (nn1+nn2)/2:
if (evalf(eval(fn3,x=temp1)) > evalf(eval(fn4,x=temp1))) then
fn5 := Int(sort(fn3-fn4), x=nn1..nn2);
else
fn5 := Int(sort(fn4-fn3), x=nn1..nn2);
end if;
elif (evalf(clow) < evalf(nn1) and evalf(chigh) > evalf(nn1) and evalf(chigh) < evalf(nn2)) then
# chlow2 < nn1 < chigh < nn2
temp2 := (nn1+chigh)/2:
if (evalf(eval(fn3,x=temp2)) > evalf(eval(fn4,x=temp2))) then
fn5 := Int(sort(fn3-fn4),x=nn1..chigh) + Int(sort(fn4-fn3),x=chigh..nn2);
else
fn5 := Int(sort(fn4-fn3),x=nn1..chigh) + Int(sort(fn3-fn4),x=chigh..nn2);
end if;
elif (evalf(clow) > evalf(nn1) and evalf(clow) < evalf(nn2)) then
if (evalf(chigh) > evalf(nn2)) then
# nn1 < clow < nn2 < chigh
temp3 := (nn1 + clow)/2:
if (evalf(eval(fn3,x=temp3)) > evalf(eval(fn4,x=temp3))) then
fn5 := Int(sort(fn3-fn4),x=nn1..clow) + Int(sort(fn4-fn3),x=clow..nn2);
else
fn5 := Int(sort(fn4-fn3),x=nn1..clow) + Int(sort(fn3-fn4),x=clow..nn2);
end if;
else
# nn1 < cnlow2 < chigh < nn2
temp4 := (nn1 + clow)/2:
if (evalf(eval(fn3,x=temp4)) > evalf(eval(fn4,x=temp4))) then
fn5 := Int(sort(fn3-fn4),x=nn1..clow) + Int(sort(fn4-fn3),x=clow..chigh) + Int(sort(fn3-fn4),x=chigh..nn2);
else
fn5 := Int(sort(fn4-fn3),x=nn1..clow) + Int(sort(fn3-fn4),x=clow..chigh) + Int(sort(fn4-fn3),x=chigh..nn2);
end if;
end if;
end if;
ans2 := fn5;JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 27.2</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.Qual \303\251 a \303\241rea da regi\303\243o entre y = `$fn3` (vermelha) e y = `$fn4` (verde) no intervalo [`$nn1`,`$nn2`]?
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JSFH
<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.evalf(value(ans2));
<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`-`$RESPONSE`), 5 ) = 0 );
<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional.
Enter your hints in the following table. You can provide up to three hints.
Do y = `$fn3` and y = `$fn4` intersect within the given interval?Replace this text with hint 2.Replace this text with hint 3.
with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Do y = </mtext><mtext></mtext><mrow><mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>1</mn></mrow></mrow><mtext></mtext><mtext> and y = </mtext><mtext>`$fn4`</mtext><mtext> intersect within the given interval?</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 `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.The definite integral is `$ans2` = `$ANSWER`with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea1`, `value`); ANSWER := evalf(value(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>95.83333333</mn></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>The definite integral is </mtext><mtext></mtext><mrow><mrow><msubsup superscriptshift='2'><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&int;</mo><mn>3</mn><mn>4</mn></msubsup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>7</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>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</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>95.83333333</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>95.83333333</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 27.3: Cortes Horizontais </Text-field>A regi\303\243o limitada pela reta horizontal LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4=, a curvay = f2;e a curvay = g2;esquematizada na Figura 27.4,
plot([1,f2,g2], x=0..1, color=[black,red,blue]);
Figura 27.4 Exemplo 27.3: Gr\303\241ficos de 1 (preto), LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic= (vermelho), e 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 (azul)
Acima fica o gr\303\241fico de 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 (em azul, na Figura 27.4) para x em 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 e abaixo o gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkmbXNxcnRHRiQ2Iy1GLDYlUSJ4RidGNEY3RitGPkYrRj4= (em vermelho, na Figura 27.4) para x em 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. Usando divis\303\265es verticais, esta \303\241rea pode ser representada como a soma de duas integrais, a saber,A_v := Int( 1-g2, x=0..T ) + Int( 1-f2, x=T..1 ):
Area = A_v;O valor desta integrais \303\251 ent\303\243oA_v = value( eval( A_v, T=T_approx ) );Esta \303\241rea pode ser representada como uma \303\272nica integral definida se divis\303\265es horizontais forem usadas. Para trabalhar com divis\303\265es horizontais, requer escrever os contornos \303\240 esquerda e \303\240 direita como fun\303\247\303\265es (functions) de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. O contorno esquerdo \303\251 formado pelo gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkmbXNxcnRHRiQ2Iy1GLDYlUSJ4RidGNEY3RitGPkYrRj4= , ouleft3 := solve( y=f2, x ):
x = left3;O contorno direito \303\251 formado pelo gr\303\241fico de 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 , ouright3 := solve( y=g2, x ):
x = right3;Designando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= a coordenada-y do ponto de interse\303\247\303\243o dos dois gr\303\241ficos, a saber,S_exact := simplify( eval( g2, x=T_exact ) ):
S_approx := evalf( S_exact ):
S = S_exact;
`` = S_approx;Note que este valor pode tamb\303\251m ser obtido resolvendo (solving) a equa\303\247\303\243oq1 := left3 = right3:
q1;para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, e obtendoq2 := solve( q1, y ):
q2 = simplify( q2 );A Figura 27.5 contendo uma esquema da desejada regi\303\243o com os contornos \303\241 sua esquerda, direita e acima destacados (highlighted) em azul, amarelo, e vermelho, respectivamente.
Figura 27.5 Exemplo 27.3: A integra\303\247\303\243o sobre a regi\303\243o contornada pelas curvas em azul (esquerda), amarelo (direito) e coral (acima)
A \303\241rea desta regi\303\243o pode agora ser escrita como uma \303\272nica integral definidaA_h := Int( left3-right3, y=S..1 ):
Area = A_h;cujo valor \303\251A_v = value( eval( A_h, S=S_approx ) );Felizmente, as duas abordagens para encontrar a \303\241rea desta regi\303\243o est\303\243o em concord\303\242ncia
<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 := `$myvariable`. Adding algorithmic variables to the question is optional.
In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.randomize():
with(plots):
with(RandomTools):
a1 := Generate(integer(range=1..3)):
c1 := Generate(integer(range=1..3)):
fn6 := a1*x+c1;
a2 := Generate(integer(range=-5..-1)):
c2 := Generate(integer(range=10..20)):
while (c2 <= c1) do c2 := Generate(integer(range=2..6)) end do:
fn7 := a2*x^2+10*x+c2;
ss2 := solve(fn6-fn7=0,x):
if (evalf(ss2[1]>ss2[2])) then
thigh3 := ss2[1];
tlow3 := ss2[2];
else
thigh3 := ss2[2];
tlow3 := ss2[1];
end if:
low3 := solve(diff(fn7,x)=0,x);
fn8 := eval(fn7,x=low3);
high3 := (solve(fn8-fn6,x));
ylow3 := simplify(eval(fn6,x=thigh3));
ry3 := solve(y=fn6,x);
ly3 := (-10-sqrt(100-4*a2*(c2-y)))/2/a2;
A3 := Int(ry3-ly3,y=ylow3..fn8);
ans3 := simplify(value(A3));
evalf(ans3);
#plot([fn6,fn7,fn8],x=low3..high3,y=0..fn8+1);
JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 27.3</Font></Text-field>The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component.
In the following text region, enter the full contents of the question.Usando divis\303\265es horizontais, encontre a \303\241rea da regi\303\243o limitada por
y = `$fn6`,
y = `$fn7`, e
y = `$fn8`
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
<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 `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.JSFHevalf(ans3);
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$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(`$ANSWER`-`$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.
Replace this text with hint 1.Replace this text with hint 2.Replace this text with hint 3.
<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.The definite integral is `$A3` = `$ANSWER`with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea2`, `value`); ANSWER := evalf(ans3); if evalb(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>12.52999121</mn></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>The definite integral is </mtext><mtext></mtext><mrow><mrow><msubsup superscriptshift='2'><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&int;</mo><mrow><mfrac><mn>29</mn><mn>8</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>3</mn><mn>8</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>193</mn></msqrt></mrow></mrow></mrow><mfrac><mn>65</mn><mn>4</mn></mfrac></msubsup><mfenced open='(' close=')' separators=','><mrow><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><mi>y</mi></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mn>19</mn><mn>12</mn></mfrac><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><msqrt><mrow><mn>65</mn><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>y</mi></mrow></mrow></msqrt></mrow></mrow></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>y</mi></mrow></mrow><mtext></mtext><mtext> = </mtext><mrow><mn>12.52999121</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>12.52999121</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 27.4: \303\201</Font><Hyperlink linktarget="Dictionary:Definition,area" hyperlink="true"><Font style="Heading 1">rea</Font></Hyperlink> de uma Elipse </Text-field>A \303\241rea de uma elipse com eixos de comprimento LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRImFGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRImJGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= \303\251 a \303\241rea limitada pelo gr\303\241fico deq3 := (x/a)^2 + (y/b)^2 = 1:
q3;A parte superior desta elipse \303\251 dada pela fun\303\247\303\243otop4 := solve( q3, y )[1];Enquanto que a metade direita desta elipse \303\251dada pela fun\303\247\303\243oright4 := solve( q3, x )[1];Usando simetria, a \303\241rea total dentro da elipse \303\251 ent\303\243oA_ell_v := 4 * Int( top4, x=0..a ):
A_ellipse = A_ell_v;onde faixas verticais foram usadas para formular esta integral definida.Esta integral (integral) pode ser avaliada, por\303\251m, n\303\243o usando as t\303\251cnicas de integra\303\247\303\243o (integration) discutidas neste curso. A chave \303\251 o fator (factor) 4 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSJhRidGN0Y6Rj0vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkkvJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y9 fora da integral e observar que a integral definida restanteq4 := Int( sqrt( a^2-x^2 ), x=0..a ):
q4;\303\251 um quarto da \303\241rea de um c\303\255rculo (circle) com raio (radius) a. Este valor \303\251q4 = value( q4 ) assuming a>0;Como resultado, a \303\241rea de uma elipse com eixos de comprimentos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRImFGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRImJGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYsNiVRJ2VsaXBzZUYnRjVGOC9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRkA= = 4 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSJhRidGN0Y6Rj0vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkkvJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y9 (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 ) = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUScmIzk2MDtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjcvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLUYsNiVRImFGJy9GNVEldHJ1ZUYnL0Y4USdpdGFsaWNGJ0Y6LUYsNiVRImJGJ0ZURlZGN0YrRjc=.Note que esta f\303\263rmula se reduz \303\240 \303\241rea de um c\303\255rculo com raio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRImJGJ0Y0RjdGPkYrRj4=. Note tamb\303\251m que este resultado poderia ter sido obtido com divis\303\265es horizontais. A integral definida para esta abordagem \303\251A_ell_h := 4 * Int( right4, y=0..b ):
A_ellipse = A_ell_h;A avalia\303\247\303\243o desta integral \303\251 quase id\303\252ntica \303\240quela encontrada com divis\303\265es verticais. O fator 4 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSJiRidGN0Y6Rj0vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkkvJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y9 externo, reconhecer a integral restante como um quarto da \303\241rea de um c\303\255culo com raio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e simplificar para obterA_ellipse = A_ell_h;
`` = value( A_ell_h ) assuming a>0, b>0;Como o esperado, os dois m\303\251todos de divis\303\243o levam ao mesmo resultado
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Sum\303\241rio</Font></Text-field>A computa\303\247\303\243o de \303\241reas \303\251 uma das aplica\303\247\303\265es fundamentais da integral definida. Um integral definida para a \303\241rea de uma regi\303\243o plana pode ser encontrada pela adi\303\247\303\243o de uma cole\303\247\303\243o apropriada de finas fatias horizontais ou verticais. O integrando (integrand) \303\251 o comprimento de cada fatia e os limites de integra\303\247\303\243o correspondem aos menores e maiores valores da vari\303\241vel independente (independent variable) que descreve a regi\303\243o.A \303\241rea de uma regi\303\243o verticalmente simples descrita 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 para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJmxlO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInhGJ0Y0RjdGPkYrRj4=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkjbW9HRiQ2LVElJmxlO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUYsNiVRImJGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU=\303\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 \303\241rea de uma regi\303\243o horizontalmente simples (horizontally simple region) descrita 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUkjbW9HRiQ2LVElJmxlO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUklbXN1YkdGJDYlLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRictRiM2JC1GLDYlUShkaXJlaXRhRidGUkZVRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRjVGK0Y1 para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJjRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJmxlO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInlGJ0Y0RjdGPkYrRj4=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkjbW9HRiQ2LVElJmxlO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUYsNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU=\303\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Embora seja importante ser capaz de avaliar uma integral definida por uma \303\241rea, o passo que requer mais habilidade e compreens\303\243o \303\251 surgir com (construir?)(coming up with) a integral.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Qual \303\251 o Pr\303\263ximo?</Font></Text-field>O pr\303\263ximo cap\303\255tulo nesta unidade considera \303\241rea na interpreta\303\247\303\243o gr\303\241fica do Teorema do Valor M\303\251dio (Mean Value Theorem) para Integrais. Neste cap\303\255tulo o valor m\303\251dio de uma fun\303\247\303\243o ser\303\241 desenvolvido usando o processo dividir em fatias, aproximar, limitar e avaliar. Os cap\303\255tulos restantes, nesta unidade, usam o mesmo processo geral para desenvolver propriedades adicionais geom\303\251tricas e f\303\255sicas de integrais definidas.Chapter Navigation<< Prev1234567891011121314151617181920212223242526 27 28293031Next >>
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