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<Text-field style="Heading 1" layout="Normal">integral definida,</Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">n.</Font> <Font bold="true">1.</Font><Font encoding="UTF-8"> (informalmente) a express\303\243o para a evolu\303\247\303\243o da  </Font><Hyperlink linktarget="Dictionary:Definition/indefiniteintegral" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">integral indefinida</Font></Hyperlink><Font encoding="UTF-8"> para uma fun\303\247\303\203o positiva entre dois  </Font><Hyperlink linktarget="Dictionary:Definition/limitofintegration" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">limites de integra\303\247\303\243o</Font></Hyperlink><Font encoding="UTF-8">, representando a \303\241rea entre o gr\303\241fico da fun\303\247\303\243o dada no eixo </Font><Font italic="true">x </Font> entre o valor de  <Font italic="true">x.</Font><Font encoding="UTF-8">  Se os limites indicados da integra\303\247\303\243o s\303\243o </Font><Font italic="true">a, b</Font><Font encoding="UTF-8">\342\200\213\342\200\213, e no intervalo [</Font><Font italic="true">a, b</Font><Font encoding="UTF-8">] \303\251 dividido em n subintervalos iguais de largura  </Font><Font family="MaplePi">d</Font> <Font italic="true">x</Font>,  em seguida, como mostrado,</Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">a regi\303\243o sombreada azul \303\251 o limite em que n tende para infinito de a soma das \303\241reas dos rect\303\242ngulos constru\303\255dos em cada subintervalo com a altura  </Font><Font italic="true">f</Font>(<Font italic="true">x</Font>)  para somar <Font italic="true">x</Font><Font encoding="UTF-8"> em que subintervalo; estes s\303\243o conhecidos como </Font><Font italic="true">elementos</Font><Font encoding="UTF-8">  da \303\241rea, do qual o rect\303\242ngulo vermelho sombreada \303\251 um exemplo. Este limite \303\251 escrito int(f(x),x=a..b) </Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">e \303\251 avaliado como </Font><Font italic="true">F</Font>(<Font italic="true">b</Font>) - <Font italic="true">F</Font>(<Font italic="true">a</Font>), onde <Font italic="true">f</Font>(<Font italic="true">x</Font><Font encoding="UTF-8">) \303\251 a fun\303\247\303\243o dada, </Font><Font italic="true">x</Font> = <Font italic="true">a</Font> e <Font italic="true">x</Font> = <Font italic="true">b</Font><Font encoding="UTF-8">  s\303\243o os limites da integra\303\247\303\243o, e </Font><Font italic="true">F</Font>(<Font italic="true">x</Font><Font encoding="UTF-8">) \303\251 a integral indefinida  <Font family="MaplePi">\303\262</Font></Font> <Font italic="true">f</Font>(<Font italic="true">x</Font><Font encoding="UTF-8">) dx.  Veja tamb\303\251mso </Font><Hyperlink linktarget="Dictionary:Definition/fundamentaltheoremofcalculus" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">teorema fundamental do c\303\241lculo</Font></Hyperlink>. <Font bold="true">2.</Font><Font encoding="UTF-8"> o valor real de uma express\303\243o. </Font><Font bold="true">3.</Font> (mais apropriadamente) <Font bold="true">a.</Font><Font encoding="UTF-8"> o integral definido \303\251 dito que existe no sentido do </Font><Hyperlink linktarget="Dictionary:Definition/Riemannintegral" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">integral de Riemann</Font></Hyperlink>, ou de outro modo, se o limite adequado de <Hyperlink linktarget="Dictionary:Definition/Darbouxsum" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">somas de Darboux</Font></Hyperlink><Font encoding="UTF-8">  existe. A integral definida de uma fun\303\247\303\243o cont\303\255nua positiva entre a e b, em seguida, d\303\241 a \303\241rea delimitada pela curva eo eixo entre esses limites. Para gerais fun\303\247\303\265es cont\303\255nuas, a integral \303\251 a soma alg\303\251brica dos espa\303\247os fechados acima e abaixo do eixo x, onde o \303\272ltimo tem sinal negativo. </Font><Font bold="true">b.</Font><Font encoding="UTF-8"> mais geralmente, a integral definida de uma fun\303\247\303\243o \303\251 dito que existe se o </Font><Hyperlink linktarget="Dictionary:Definition/Lebesgueintegral" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">Lebesgue integral</Font></Hyperlink><Font encoding="UTF-8"> do produto da fun\303\247\303\243o com o </Font><Hyperlink linktarget="Dictionary:Definition/characteristicfunction" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">fun\303\247\303\243o caracter\303\255sticas</Font></Hyperlink><Font encoding="UTF-8"> para que existe intervalo, isto \303\251, desde que a fun\303\247\303\243o pode ser aproximada por fun\303\247\303\265es simples mensur\303\241veis\342\200\213\342\200\213. Se a fun\303\247\303\243o \303\251 cont\303\255nua, em seguida, o que d\303\241 o integral de Riemann como o limite da  </Font><Hyperlink linktarget="Dictionary:Definition/Darbouxsum" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">soma de Darboux</Font></Hyperlink>.</Text-field>
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