<Text-field style="Heading 1" layout="Heading 1">Introdu\303\247\303\243o</Text-field>

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Cap\303\255tulo 28

Teorema do Valor M\303\251dio Para Integrais

O Teorema do Valor M\303\251dio para Integrais \303\251 uma conseq\303\274\303\252ncia direta do Teorema do Valor M\303\251dio (para derivadas) e os Teoremas Fundamentais de C\303\241lculo. Resumindo, o TVM para integrais declara que uma fun\303\247\303\243o cont\303\255nua em um intervalo limitado e fechado tem pelo menos um ponto onde ela \303\251 igual ao seu valor m\303\251dio no intervalo. A interpreta\303\247\303\243o geom\303\251trica \303\251 que a \303\241rea sob o gr\303\241fico de uma fun\303\247\303\243o cont\303\255nua em um intervalo limitado e fechado \303\251 igual a \303\241rea de um ret\303\242ngulo cuja base \303\251 o comprimento do intervalo e a altura \303\251 o valor do integrando em algum ponto no intervalo.

O maplet FunctionAverage (que \303\251 justamente o j\303\241 imbutido Tutor M\303\251dia de Fun\303\247\303\265es, pode ser usado para fazer o gr\303\241fico de uma fun\303\247\303\243o, estabelecer a integral definida para o valor m\303\251dio em um intervalo e visualizar a conclus\303\243o do TVM para Integrais. Este maplet \303\251 constru\303\255do junto ao comando FunctionAverage no pacote Student[Calculus1].

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">\303\215ndice de Termos</Text-field>

Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio do Maple; para mais informa\303\247\303\265es v\303\241 em Dicion\303\241rio Matem\303\241tico.

\303\241rea

constante

cont\303\255nuo

integral definida

derivada

diferenciavel

descontinuidade

par

ponto flutuante

fun\303\247\303\243o

teorema fundamental do c\303\241lculo

gr\303\241fico

hip\303\263tese

integrando

intervalo

continuidade de salto

m\303\241ximo

teorem do valor m\303\251dio

m\303\255nimo

teorema do valor m\303\251dio

per\303\255odo

fun\303\247\303\243o definida por trecho

prova

real

Soma de Riemann

resolver

valor

volume

trabalho

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Inicializa\303\247\303\243o</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnRitGOkY9

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

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Teorema do <Hyperlink linktarget="Wks:../Dicion\303\241rio/V/value.mw" hyperlink="true" encoding="UTF-8">Valor M\303\251dio para Integrais</Hyperlink></Text-field>

Teorema 28.1 \303\251 um um enunciado formal do Teorema do Valor M\303\251dio para Integrais.

Teorema 28.1: Teorema do Valor M\303\251dio para Integrais

Se f \303\251 uma fun\303\247\303\243o cont\303\255nua do intervalo limitado e fechado 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, ent\303\243o existe pelo menos um n\303\272mero LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em 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 para o qual:

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

\303\251 verdadeiro.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Prova do Teorema 28.1</Text-field>

A prova do TVM para Integrais \303\251 uma aplica\303\247\303\243o do TVM para derivadas, com uma escolha apropriada da fun\303\247\303\243o. Para cada valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em 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, define-se a fun\303\247\303\243o F pela regra:

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

O Primeiro Teorema Fundamental de C\303\241lculo nos diz que F \303\251 cont\303\255nua em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYmLUYsNiVRImFGJy8lJ2l0YWxpY0dGOi9GNlEnaXRhbGljRictRjI2LVEiLEYnRjUvRjlGPS9GPEY6L0Y/Rj1GQEZCRkRGRi9GSVEmMC4wZW1GJy9GTFEsMC4zMzMzMzMzZW1GJy1GLDYlUSJiRidGUkZURjUtRjI2LVEiXUYnRjVGOEY7Rj5GQEZCRkRGRkZIL0ZMUSwwLjExMTExMTFlbUYnRjVGK0Y1, \303\251 diferenci\303\241vel emLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiQtRiM2JkYrLUYjNiYtRiw2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GPVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGRy8lKnN5bW1ldHJpY0dGRy8lKGxhcmdlb3BHRkcvJS5tb3ZhYmxlbGltaXRzR0ZHLyUnYWNjZW50R0ZHLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRjlGPEZDRitGQ0ZDRkM=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR0Y0Ri8tRiw2LVEifkYnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRkc2JVEkdGVtRidGSkYvRkwtRkc2JVEkdW1hRidGSkYvRkxGLw==derivada dada por 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. Estas s\303\243o exatamente as condi\303\247\303\265es necess\303\241rias para aplicar o TVM a F em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYmLUYsNiVRImFGJy8lJ2l0YWxpY0dGOi9GNlEnaXRhbGljRictRjI2LVEiLEYnRjUvRjlGPS9GPEY6L0Y/Rj1GQEZCRkRGRi9GSVEmMC4wZW1GJy9GTFEsMC4zMzMzMzMzZW1GJy1GLDYlUSJiRidGUkZURjUtRjI2LVEiXUYnRjVGOEY7Rj5GQEZCRkRGRkZIL0ZMUSwwLjExMTExMTFlbUYnRjVGK0Y1. Portanto, existe pelos menos um ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkktRiM2Ji1GMjYtUSIoRidGNS9GOVEldHJ1ZUYnRjsvRj5GUkY/RkFGQ0ZFL0ZIUSwwLjE2NjY2NjdlbUYnL0ZLRlUtRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHRlIvRjZRJ2l0YWxpY0YnLUYyNi1RIixGJ0Y1RjgvRjxGUkY9Rj9GQUZDRkVGRy9GS1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJiRidGZm5GaG5GNS1GMjYtUSIpRidGNUZRRjtGU0Y/RkFGQ0ZFRlQvRktRLDAuMTExMTExMWVtRidGNUYrRjVGK0Y1 para o qual:

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

Agora, da defini\303\247\303\243o de F,

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 = 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

Logo, temos:

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 = 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 = 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

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">O Valor M\303\251dio de uma Fun\303\247\303\243o</Text-field>

Defini\303\247\303\243o 28.1 prov\303\252 o significado formal para o termo valor m\303\251dio de uma fun\303\247\303\243o.

Defini\303\247\303\243o 28.1: O Valor M\303\251dio de uma Fun\303\247\303\243o

Seja f uma fun\303\247\303\243o cont\303\255nua em um intervalo limitado e fechado 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. O valor m\303\251dio de f em 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 \303\251:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYsNiVRJGF2Z0YnRjVGOC9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRkA= = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiYtRiw2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y5USdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJ0Y4LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZNLyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmZuLUYsNiVRImFGJ0ZCRkVGOEYrRjgvJS5saW5ldGhpY2tuZXNzR0Y3LyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBvLyUpYmV2ZWxsZWRHRk1GK0Y4 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

O comando FunctionAverage no pacote Student[Calculus1] do Maple \303\251 \303\272til neste contexto.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Motiva\303\247\303\243o para a Defini\303\247\303\243o 28.1</Text-field>

Seja f uma fun\303\247\303\243o definida no intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYmLUYsNiVRImFGJy8lJ2l0YWxpY0dGOi9GNlEnaXRhbGljRictRjI2LVEiLEYnRjUvRjlGPS9GPEY6L0Y/Rj1GQEZCRkRGRi9GSVEmMC4wZW1GJy9GTFEsMC4zMzMzMzMzZW1GJy1GLDYlUSJiRidGUkZURjUtRjI2LVEiXUYnRjVGOEY7Rj5GQEZCRkRGRkZIL0ZMUSwwLjExMTExMTFlbUYnRjVGK0Y1. Considere uma parti\303\247\303\243o regular de 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 em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= subintervalos com limites (de intervalos):

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMEYnL0Y5USdub3JtYWxGJ0ZBLyUvc3Vic2NyaXB0c2hpZnRHRkBGK0ZB < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnL0Y5USdub3JtYWxGJ0ZBLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGK0ZB < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkLi4uRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== < 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 < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYsNiVRIm5GJ0Y1RjgvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGK0ZA = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=

que \303\251, para cada 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, define 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 e 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. A m\303\251dia de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= valores de fun\303\247\303\243o, 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,

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiw2JVElJm11O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGNQ==

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUYjNiotSSNtaUdGJDYjUSFGJy1JK211bmRlcm92ZXJHRiQ2Jy1GLDYvUSYmU3VtO0YnLyUrZm9yZWdyb3VuZEdRLlsxNDQsMTQ0LDE0NF1GJ0YvL0krbXNlbWFudGljc0dGJFEmaW5lcnRGJ0YyRjUvRjhRJXRydWVGJ0Y5L0Y8RlkvRj5GWUY/L0ZCUSYwLjBlbUYnL0ZFUSwwLjE2NjY2NjdlbUYnLUYjNiYtRkk2JVEiaUYnLyUnaXRhbGljR0ZZL0YwUSdpdGFsaWNGJ0YrLUkjbW5HRiQ2JFEiMUYnRi9GLy1GSTYlUSJuRidGX29GYW9GPy8lLGFjY2VudHVuZGVyR0Y0RkgtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJDUuMEYnLyUmZGVwdGhHRmFwLyUqbGluZWJyZWFrR1ElYXV0b0YnRkgtSSZtZnJhY0dGJDYoLUYjNiZGSC1GIzYnLUZJNiVRImZGJ0Zfb0Zhby1GLDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0YvRjJGNUY3RjlGO0Y9Rj9GZm4vRkVGZ24tRiM2Ji1GLDYtUSIoRidGLy9GM0ZZRjVGWEY5RjtGPUY/L0ZCRmluRmhuLUYjNiZGSC1JJW1zdWJHRiQ2JS1GSTYlUSJ4RidGX29GYW8tRiM2JEZcb0YvLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGSEYvLUYsNi1RIilGJ0YvRl1yRjVGWEY5RjtGPUY/Rl5yL0ZFUSwwLjExMTExMTFlbUYnRi9GSEYvRkhGLy1GIzYkRmdvRi8vJS5saW5ldGhpY2tuZXNzR0Zmby8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zncy8lKWJldmVsbGVkR0Y0RkhGL0ZIRi8=

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

Observe que nos \303\272ltimos dois passos, a defini\303\247\303\243o de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUScmIzkxNjtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjcvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLUYsNiVRInhGJy9GNVEldHJ1ZUYnL0Y4USdpdGFsaWNGJ0Y3RitGNw== foi usado para escrever 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 e a constante LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiYtRiw2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y5USdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJ0Y4LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZNLyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmZuLUYsNiVRImFGJ0ZCRkVGOEYrRjgvJS5saW5ldGhpY2tuZXNzR0Y3LyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBvLyUpYmV2ZWxsZWRHRk1GK0Y4 pode ser fatorada fora da soma.

A soma na \303\272ltima express\303\243o \303\251 uma soma de Riemann. Se o n\303\272mero de pontos dados \303\251 cresce sem limites, temos uma integral definida, ou seja:

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 = 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

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 28.1: <Hyperlink linktarget="Wks:../Dicion\303\241rio/H/hypothesis -.mw" hyperlink="true" encoding="UTF-8">Hip\303\263teses</Hyperlink> do TVM Satisfeitas</Text-field>

A fun\303\247\303\243o:

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que aparece na Figura 28.1,

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9$"0*ywO5(z#e!#;7$$"0Z$pQnq&*Q!#9$".1Tp&*f_&!#97$$"0c6BEeE%R!#9$"09x#Q%QDF&!#;7$$"0NpQdIo*R!#9$"0WyH^6X*\!#;7$$"0rU&3prXS!#9$"0<>8??iv%!#;7$$"0/29Q(3%4%!#9$"00KQ,N;`%!#;7$$"0Z%*)y65YT!#9$"0j!3wD&>I%!#;7$$"0d9HQD$)>%!#9$"0T4\A_I3%!#;7$$"/%zenTeC%!#8$"/hdDzd$*Q!#:7$$"0rT$o=I'H%!#9$"0:$=t=)>q$!#;7$$"06AW3YbM%!#9$"/#))f`'4CN!#:7$$"0'3<Mt#*)R%!#9$"0$GL`(34M$!#;7$$"0#Rycp6XW!#9$"0,X#yI5!>$!#;7$$"0%ze<u;)\%!#9$"0T(QNtFDI!#;7$$"0\)pRw.[X!#9$"03A!4j5yG!#;7$$"0D\)phU(f%!#9$"0T/]'RTRF!#;7$$"0sW*))R&ok%!#9$"0@L9f-tg#!#;7$$"0RycBnsp%!#9$"0<>VC="zC!#;7$$"0KjEV/2v%!#9$"0=M@]=,N#!#;7$$"0uZ&46q*z%!#9$"0[jl#fuPA!#;7$$"0`067n![[!#9$"0;@ot!4K@!#;7$$"0Hd9fp(**[!#9$"0fY#*edY-#!#;7$$"0D]+^f8&\!#9$"0$o1gU&G#>!#;7$$"#]!""$"0Ut)))QcJ=!#;-%&COLORG6'%$RGBG$"#5!""$""!!""$""!!""-%+_ATTRIBUTEG6#/%'sourceG%,mathdefaultG-%%VIEWG6$;$!#]!""$"#]!""%(DEFAULTG-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%*THICKNESSG6#""$-%%ROOTG6'-%)BOUNDS_XG6#$"#!*!""-%)BOUNDS_YG6#$"#!)!""-%-BOUNDS_WIDTHG6#$"%IQ!""-%.BOUNDS_HEIGHTG6#$"%!\$!""-%)CHILDRENG6"

Figura 28.1

Exemplo 28.1: Gr\303\241fico de 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

\303\251 cont\303\255nua para todos os n\303\272meros reais. Em particular, o TVM para Integrais se aplica no intervalo 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. O valor m\303\251dio de f 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 \303\251:

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

LyZJImZHNiI2I0kkYXZnR0YlLCQqJiMiIiIiIzVGKy1JJEludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUkqcGllY2V3aXNlR0YwNicySSJ4R0YlIiIhRjgyRjdGK0Y3LUkkZXhwR0YvNiMsJkYrRitGNyEiIi9GNzshIiYiIiZGK0Yr

L0khRzYiLCYjIiIkIiM/IiIiKiYjRikiIzVGKS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjISIlRikhIiI=

L0khRzYiJCIraFZvIlsiISM1

Quando o valor m\303\251dio est\303\241 inclu\303\255do no gr\303\241fico da fun\303\247\303\243o, a \303\241rea sombreada abaixo do valor m\303\251dio deve ser igual \303\240 \303\241rea sob a fun\303\247\303\243o. Isto \303\251 ilustrado na Figura 28.2:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEwRnVuY3Rpb25BdmVyYWdlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlMtSShtZmVuY2VkR0YkNiQtRiM2Mi1GLDYlUSNmMkYnRjZGOS1GPTYtUSIsRidGQEZCL0ZGRjhGR0ZJRktGTUZPRlEvRlVRLDAuMzMzMzMzM2VtRictRiM2KC1GLDYlUSJ4RidGNkY5LUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGZ28tRiM2KEYrLUYjNiYtRj02LVEqJnVtaW51czA7RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjIyMjIyMjJlbUYnL0ZVRmFwLUkjbW5HRiQ2JFEiNUYnRkAvJStleGVjdXRhYmxlR0ZERkAtRj02LVEjLi5GJ0ZARkJGRUZHRklGS0ZNRk9GYHBGVEZjcEZncEZARitGZ3BGQEZobi1GIzYnLUYsNiVRJ291dHB1dEYnRjZGOUZjby1GLDYlUSVwbG90RidGNkY5RmdwRkBGaG4tRiM2Jy1GLDYlUS9hdmVyYWdlb3B0aW9uc0YnRjZGOUZjby1GVzYmLUYjNilGKy1GIzYnLUYsNiVRJmNvbG9yRidGNkY5RmNvLUYsNiVRJWN5YW5GJ0Y2RjlGZ3BGQEZobi1GIzYnLUYsNiVRJ2ZpbGxlZEYnRjZGOUZjby1GLDYlRjhGNkY5RmdwRkBGK0ZncEZARkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGZ3BGQEZobi1GIzYnLUYsNiVRJXZpZXdGJ0Y2RjlGY28tRlc2Ji1GIzYoLUYsNiVRKERFRkFVTFRGJ0Y2RjlGaG4tRiM2Jy1GZHA2JFEiMEYnRkBGaXAtRmRwNiRRIjFGJ0ZARmdwRkBGK0ZncEZARkBGXHNGX3NGZ3BGQEZobi1GIzYnLUYsNiVRKnRoaWNrbmVzc0YnRjZGOUZjby1GZHA2JFEiM0YnRkBGZ3BGQEZobi1GIzYoLUYsNiVRJnRpdGxlRidGNkY5RmNvLUkjbXNHRiRGLUYrRmdwRkBGK0ZncEZARkBGZ3BGQEYrRmdwRkBGK0ZncEZA

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Figura 28.2

Valor m\303\251dio de 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

no 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

Figura 28.2 sugere que existem dois pontos no intervalo 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 onde o valor da fun\303\247\303\243o \303\251 igual ao seu valor m\303\251dio em 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. Estes dois pontos s\303\243o:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNzMkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

NiQ8Iy9JInhHNiIsJiMiIiQiIz8iIiIqJiNGKyIjNUYrLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMhIiVGKyEiIjwjL0YlLCZGK0YrLUkjbG5HRjE2IywmRihGKyomRi1GKy1GMDYjIiIlRjZGNkY2

ou, na forma de ponto flutuante,

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

NiQ8Iy9JInhHNiIkIitoVm8iWyIhIzU8Iy9GJSQiK3JiUzRIISIq

Este valores s\303\243o consistentes com o gr\303\241fico na Figura 28.2.

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</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(): dd := Generate(integer(range=3..6)): nn1 := Generate(integer(range=1..4)): lo_[1] := Generate(integer(range=-5..5)): hi_[1] := Generate(integer(range=1..10)): while (hi_[1]<=lo_[1]) do hi_[1] := Generate(integer(range=1..10)) od: fn1_[1] := sort(Generate(polynom(integer(range=-6..6),x,degree=dd)),x): nn2 := Generate(choose([2,3,4,6])): nn3 := Generate(rational(range=0..1, denominator=nn2)): nn4 := Generate(rational(range=0..2, denominator=nn2)): while (nn4<=nn3) do nn4 := Generate(rational(range=0..2, denominator=nn2)) od: lo_[2] := Pi*nn3: hi_[2] := Pi*nn4: fn1_[2] := Generate(choose([cos(nn1*x),sin(nn1*x),cos(nn1*x)*sin(nn1*x)])): nn5 := Generate(choose([1,2])): hi := hi_[nn5]: lo := lo_[nn5]: fn1 := fn1_[nn5]; DIn1 := Int(fn1,x=lo..hi)/(hi-lo); PDIn1 := eval(DIn1,Pi=`π`): ans1 := value(DIn1);

LUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInhHRic=

LCQqJi1JJEludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkkc2luR0YmNiNJInhHRikvRi47LCRJI1BpR0YnIyIiIiIiJEYyRjRGMiEiIiNGNSIiIw==

LCQqJEkjUGlHJSpwcm90ZWN0ZWRHISIiIyIiKiIiJQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 28.1</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.

Encontre o valor m\303\251dio da fun\303\247\303\243o f(x) = `$fn1` entre x = `$lo` e x = `$hi`. 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 significantes.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<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.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=eval(ans1,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( fnormal(evalf(`$ans1`-`$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.

Use the Mean Value Theorem for Integrals.

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>Use the Mean Value Theorem for Integrals.</mtext><mtext>&NewLine;</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.

f(c) = `$PDIn1` = `$ANSWER`

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea0`, `value`); ANSWER := eval(ans1,Pi=`π`); if evalb( fnormal(evalf(ans1-eval(parse(StudentResponse))), 5 ) = 0 ) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</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>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</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><mfrac><mrow><mn>9</mn></mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>&\134#x3c0;</mi></mrow></mfrac></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>f(c)</mtext><mtext> = </mtext><mtext></mtext><mrow><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfrac><mrow><mrow><msubsup superscriptshift='2'><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&int;</mo><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><mi>&\134#x3c0;</mi></mrow></mrow><mi>&\134#x3c0;</mi></msubsup><mrow><mi mathvariant='normal'>sin</mi><mo lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow><mspace height='0.0ex' width='0.3em' depth='0.0ex' linebreak='auto'/><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow><mrow><mi>&\134#x3c0;</mi></mrow></mfrac></mrow></mrow><mtext></mtext><mtext> </mtext><mtext>=</mtext><mtext> </mtext><mrow><mfrac><mrow><mn>9</mn></mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>&\134#x3c0;</mi></mrow></mfrac></mrow><mtext></mtext><mtext>&NewLine;</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><mfrac><mrow><mn>9</mn></mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>&\134#x3c0;</mi></mrow></mfrac></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 28.2: <Hyperlink linktarget="Wks:../Dicion\303\241rio/H/hypothesis -.mw" hyperlink="true" encoding="UTF-8">Hip\303\263teses</Hyperlink> de TVM N\303\243o S\303\243o Satisfeitas</Text-field>

A fun\303\247\303\243o constante por partes:

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Cujo gr\303\241fico aparece na Figura 28.3:

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Figura 28.3

Exemplo 28.2: Gr\303\241fico de 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

tem descontinuidades de salto em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMkYnRj5GPkYrRj4=. Como f n\303\243o \303\251 cont\303\255nua em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMkYnRj5GPkYrRj4=, o TVM para Integrais n\303\243o se aplica no intervalo 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.

Para compreender o porqu\303\252 a conclus\303\243o de que o TVM para Integrais n\303\243o \303\251 satisfeita, observe que o valor m\303\251dio de f em 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 \303\251:

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

LywkKiYjIiIiIiInRiYtSSRJbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC1JKnBpZWNld2lzZUdGKzYnMkkieEdGLSIiISEiIjJGMyIiI0Y3RiYvRjM7ISIkIiIkRiZGJiNGJkY7

Como os valores da fun\303\247\303\243o s\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZJLUkjbW5HRiQ2JFEiMUYnRjVGNS1GMjYtUSIsRidGNUY4L0Y8USV0cnVlRidGPUY/RkFGQ0ZFRkcvRktRLDAuMzMzMzMzM2VtRidGTEY1, e 2, est\303\241 claro que n\303\243o existem pontos em 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 onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiQtSShtZmVuY2VkR0YkNiQtRiM2JkYrLUYjNiQtRiw2JVEieEYnRjZGOUZARitGQEZARkBGK0ZALUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGYG8tSSVtc3ViR0YkNiVGMy1GIzYkLUYsNiVRK20mIzIzMztkaW9GJ0Y2RjlGQC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRitGQEYrRkA= = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JC1GNTYkUSIzRidGOEY4LyUubGluZXRoaWNrbmVzc0dGNy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZELyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== . Veja a Figura 28.4 para uma representa\303\247\303\243o concreta desta conclus\303\243o.

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dulenameG6"I,TypesettingGI(_syslibG6"66-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"66Q"x6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%0font_style_nameGQ%Text6"/%,mathvariantGQ'italic6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#126"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%0font_style_nameGQ%Text6"/%,mathvariantGQ'normal6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%0font_style_nameGQ%Text6"/%,mathvariantGQ'normal6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#126"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%0font_style_nameGQ%Text6"/%,mathvariantGQ'normal6"-%-TRANSPARENCYG6#$""!!""-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"$q#!""-%-BOUNDS_WIDTHG6#$"%!z$!""-%.BOUNDS_HEIGHTG6#$"%I@!""-%)CHILDRENG6"

Figura 28.4

Valor m\303\251dio de 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

no 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

Qualquer esfor\303\247o para resolver encontrar o ponto onde 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 alcan\303\247a seu valor m\303\251dio est\303\241 destinado a falhar, como mostra o resultado nulo dos c\303\241lculos do Maple:

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

Note que o valor m\303\251dio da fun\303\247\303\243o em 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 \303\251:

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

LywkKiYjIiIiIiIlRiYtSSRJbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC1JKnBpZWNld2lzZUdGKzYnMkkieEdGLSIiISEiIjJGMyIiI0Y3RiYvRjM7RjUiIiRGJkYmRiY=

Agora, como o valor m\303\251dio da fun\303\247\303\243o em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYnRistRiM2JS1GMjYtUSomdW1pbnVzMDtGJ0Y1L0Y5Rj1GOy9GP0Y9RkBGQkZERkYvRklRJjAuMGVtRicvRkxGVy1JI21uR0YkNiRRIjFGJ0Y1RjUtRjI2LVEiLEYnRjVGVC9GPEY6RlVGQEZCRkRGRkZWL0ZMUSwwLjMzMzMzMzNlbUYnLUZaNiRRIjNGJ0Y1RjUtRjI2LVEiXUYnRjVGOEY7Rj5GQEZCRkRGRkZIL0ZMUSwwLjExMTExMTFlbUYnRjVGK0Y1 \303\251 um dos valores desta fun\303\247\303\243o, existem pontos onde o valor da fun\303\247\303\243o coincide com o valor m\303\251dio em 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. Isto pode ser visto graficamente na Figura 28.5.

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255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%0font_style_nameGQ%Text6"/%,mathvariantGQ'normal6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%0font_style_nameGQ%Text6"/%,mathvariantGQ'normal6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#126"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%0font_style_nameGQ%Text6"/%,mathvariantGQ'normal6"-%-TRANSPARENCYG6#$""!!""-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"$q#!""-%-BOUNDS_WIDTHG6#$"%!z$!""-%.BOUNDS_HEIGHTG6#$"%I@!""-%)CHILDRENG6"

Figura 28.5

Valor m\303\251dio de 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

no 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

Pode ser visto tamb\303\251m algebricamente atrav\303\251s da seguinte computa\303\247\303\243o:

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

PCMxIiIjSSJ4RzYi

Mesmo que TVM para Integrais n\303\243o se aplica em 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 or LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYnRistRiM2JS1GMjYtUSomdW1pbnVzMDtGJ0Y1L0Y5Rj1GOy9GP0Y9RkBGQkZERkYvRklRJjAuMGVtRicvRkxGVy1JI21uR0YkNiRRIjFGJ0Y1RjUtRjI2LVEiLEYnRjVGVC9GPEY6RlVGQEZCRkRGRkZWL0ZMUSwwLjMzMzMzMzNlbUYnLUZaNiRRIjNGJ0Y1RjUtRjI2LVEiXUYnRjVGOEY7Rj5GQEZCRkRGRkZIL0ZMUSwwLjExMTExMTFlbUYnRjVGK0Y1, n\303\243o \303\251 uma contradi\303\247\303\243o encontrar um caso onde a conclus\303\243o \303\251 verdadeira mesmo quando as hip\303\263teses s\303\243o falsas. (Em termos de l\303\263gica booleana: Falso implica que Verdade \303\251 uma declara\303\247\303\243o verdadeira).

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 28.3: Respira\303\247\303\243o Humana</Text-field>

A fun\303\247\303\243o de respirar, essencial \303\240 vida, \303\251 c\303\255clica. Em repouso, uma pessoa em boa forma completar\303\241 aproximadamente 10 ciclos respirat\303\263rios completos a cada minuto. A taxa m\303\241xima de ar fluindo para os pulm\303\265es \303\251 cerca de meio litro por segundo. Baseando-se nestas suposi\303\247\303\265es:

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

IiM1

IyIiIiIiIw==

a raz\303\243o de ar fluindo para os pulm\303\265es pode ser modelado pela fun\303\247\303\243o:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVElcmF0ZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtRiM2Jy1GLDYlUTVtYXhfcmF0ZV9vZl9haXJfZmxvd0YnRjZGOS1GPTYtUTEmSW52aXNpYmxlVGltZXM7RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSYwLjBlbUYnL0ZVRmluLUYjNictRiw2JVEkc2luRicvRjdGREZALUY9Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRkBGQkZFRkdGSUZLRk1GT0ZobkZqbi1JKG1mZW5jZWRHRiQ2JC1GIzYnRistRiM2Ki1JI21uR0YkNiRRIjJGJ0ZARmVuLUYsNiVRJyYjOTYwO0YnRmBvRkBGZW4tRiw2JVEieEYnRjZGOUZlbi1JJm1mcmFjR0YkNigtRiM2JS1GLDYlUTpudW1fcmVzcF9jeWNsZV9wZXJfbWludXRlRidGNkY5LyUrZXhlY3V0YWJsZUdGREZALUYjNiUtRlxwNiRRIzYwRidGQEZdcUZALyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZpcS8lKWJldmVsbGVkR0ZERkBGK0ZdcUZARkBGXXFGQEYrRkBGK0ZdcUZARitGXXFGQC1GPTYtUSI6RidGQEZCRkVGR0ZJRktGTUZPRlFGVEZdcUZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNihGKy1GIzYnLUYsNiVRImZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GPFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkYvJSlzdHJldGNoeUdGRi8lKnN5bW1ldHJpY0dGRi8lKGxhcmdlb3BHRkYvJS5tb3ZhYmxlbGltaXRzR0ZGLyUnYWNjZW50R0ZGLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVS1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInRGJ0Y4RjsvJStleGVjdXRhYmxlR0ZGRkJGQkZqbkZCLUY/Ni1RIj1GJ0ZCRkRGR0ZJRktGTUZPRlEvRlRRLDAuMjc3Nzc3OGVtRicvRldGYG8tRiw2JVElcmF0ZUYnRjhGO0ZqbkZCRitGam5GQkYrRmpuRkI=

Ly1JImZHNiI2I0kidEdGJSwkKiYjIiIiIiIjRistSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywkKigjRisiIiRGK0kjUGlHRjBGK0kieEdGJUYrRitGK0Yr

O volume (em litros) de ar nos pulm\303\265es pelo tempo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= (em segundos) \303\251:

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

Ly1JIlZHNiI2I0kidEdGJS1JJEludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLCQqJiMiIiIiIiNGMS1JJHNpbkdGKjYjLCQqKCNGMSIiJEYxSSNQaUdGK0YxSSJ4R0YlRjFGMUYxRjEvRjs7IiIhRic=

L0khRzYiLCQqKCMiIiQiIiMiIiIsJkYqISIiLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJCooI0YqRihGKkkjUGlHRjBGKkkidEdGJEYqRipGKkYqRjZGLEYs

A rela\303\247\303\243o entre a taxa de air fluindo e o volume de ar nos pulm\303\265es \303\251 mostrado claramente na Figura 28.6.

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Figura 28.6

Exemplo 28.3: Gr\303\241fico da raz\303\243o de ar fluindo e o volume de ar nos pulm\303\265es

Observe que o volume \303\251 peri\303\263dico, com per\303\255odo de 6 segundos, e que a quantidade m\303\241xima de ar nos pulm\303\265es \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIzRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JC1GLDYlUScmIzk2MDtGJy8lJ2l0YWxpY0dRJmZhbHNlRidGOEY4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZILyUpYmV2ZWxsZWRHRkJGK0Y4 L, ou aproximadamente 0.9549 L. O m\303\241ximo ocorre a cada tempo 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 ; o valor m\303\255nimo, 0 L, \303\251 atingido a cada tempo 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. (Durante tempos de exerc\303\255cios ou outros processos estressantes a respira\303\247\303\243o aumenta; a capacidade m\303\241xima do pulm\303\243o \303\251 cerca de 3.7 L.)

A quantidade m\303\251dia de ar nos pulm\303\265es durante um ciclo completo de uma respira\303\247\303\243o \303\251:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVEoYXZnX3ZvbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtRiM2Jy1GLDYlUTBGdW5jdGlvbkF2ZXJhZ2VGJ0Y2RjktRj02LVEwJkFwcGx5RnVuY3Rpb247RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSYwLjBlbUYnL0ZVRmluLUkobWZlbmNlZEdGJDYkLUYjNiotRiw2JVEkdm9sRidGNkY5LUY9Ni1RIixGJ0ZARkIvRkZGOEZHRklGS0ZNRk9GaG4vRlVRLDAuMzMzMzMzM2VtRictRiM2KC1GLDYlUSJ0RidGNkY5LUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk9GUUZULUYjNictSSNtbkdGJDYkUSIwRidGQC1GPTYtUSMuLkYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yMjIyMjIyZW1GJ0Zqbi1GZHA2JFEiNkYnRkAvJStleGVjdXRhYmxlR0ZERkBGK0ZfcUZARmNvLUYjNictRiw2JVEnb3V0cHV0RidGNkY5Rl5wLUYsNiVRKWludGVncmFsRidGNkY5Rl9xRkBGK0ZfcUZARkBGX3FGQEYrRl9xRkBGK0ZfcUZALUY9Ni1RIjpGJ0ZARkJGRUZHRklGS0ZNRk9GUUZURl9xRkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictSSVtc3ViR0YkNiUtRiw2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYsNiVRJGF2Z0YnRjlGPC8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y9USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiPUYnRkcvJSZmZW5jZUdGRi8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zqbi1GLDYlUShhdmdfdm9sRidGOUY8RkRGR0YrRkRGRy1GTTYtUSI7RidGR0ZQL0ZTRjtGVEZWRlhGWkZmbi9GaW5RJjAuMGVtRidGW29GREZHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVEjYGBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtRiM2Jy1GLDYlUSZ2YWx1ZUYnRjZGOS1GPTYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRJjAuMGVtRicvRlVGaW4tSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUShhdmdfdm9sRidGNkY5LyUrZXhlY3V0YWJsZUdGREZARkBGY29GQEYrRmNvRkBGK0Zjb0ZALUY9Ni1RIjtGJ0ZARkIvRkZGOEZHRklGS0ZNRk9GaG5GVEZjb0ZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVEjYGBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtRiM2Jy1GLDYlUSZldmFsZkYnRjZGOS1GPTYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRJjAuMGVtRicvRlVGaW4tSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUShhdmdfdm9sRidGNkY5LyUrZXhlY3V0YWJsZUdGREZARkBGY29GQEYrRmNvRkBGK0Zjb0ZARitGY29GQA==

LyZJIlZHNiI2I0kkYXZnR0YlLCQqJiMiIiIiIidGKy1JJEludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLCQqKCMiIiQiIiNGKywmRishIiItSSRjb3NHRi82IywkKigjRitGNkYrSSNQaUdGMEYrSSJ0R0YlRitGK0YrRitGQEY5RjkvRkE7IiIhRixGK0Yr

L0khRzYiLCQqJiMiIiQiIiMiIiJJI1BpRyUqcHJvdGVjdGVkRyEiIkYq

L0khRzYiJCIrJUhbWXglISM1

A quantidade m\303\251dia de ar nos pulm\303\265es durante cada ciclo respirat\303\263rio (quando em repouso) \303\251 um pouco abaixo de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JC1GNTYkUSIyRidGOEY4LyUubGluZXRoaWNrbmVzc0dGNy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZELyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== L. A Figura 28.7 exibe esta informa\303\247\303\243o graficamente.

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Figura 28.7 Quantidade m\303\251dia de ar nos pulm\303\265es durante o ciclo respirat\303\263rio

Note que o valor m\303\251dio n\303\243o \303\251 taxa m\303\241xima do ar que flui. Numericamente as duas quantidades est\303\243o pr\303\263ximas, mas os valores (e as unidades) s\303\243o diferentes.

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Resumo</Text-field>

O Teorema do Valor M\303\251dio para integrais \303\251 obtido quando o TVM para derivadas \303\251 aplicado \303\240 fun\303\247\303\243o 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 no intervalo 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. Esta vers\303\243o do TVM prov\303\252 condi\303\247\303\265es quando \303\251 assegurado que a fun\303\247\303\243o tem o seu valor m\303\251dio para os ponto(s) no intervalo. Equivalentemente, \303\251 garantido haver pelo menos um n\303\272mero c 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 para o qual:

\303\251 verdadeiro.

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Pr\303\263ximo Cap\303\255tulo</Text-field>

As aplica\303\247\303\265es restantes nesta unidade -- C\303\241lculo de Volumes, Comprimento de Arco, e Trabalho (mec\303\242nico) -- podem ser vistas em qualquer ordem.

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