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abp2u
 2 years ago
Integration: (pi/4) to (pi/4) cos x dx
abp2u
 2 years ago
Integration: (pi/4) to (pi/4) cos x dx

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ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0Do you know the Fundamental Theorem of Calculus?

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.0note that \(\int cos x dx= sin x +C\)

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0It says\[\int\limits_{a}^{b}f(x)dx=F(a)F(b)\]In this case this means: (see also the answer of Shadowys)\[\int\limits_{\frac{ \pi }{ 4 }}^{\frac{ \pi }{ 4 }}cosxdx=\sin(\frac{ \pi }{ 4 })\sin( \frac{ \pi }{ 4 })=\frac{ 1 }{ 2 }\sqrt{2}\frac{ 1 }{ 2 }\sqrt{2}=\sqrt{2}\]

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0F is called a primitive function of f. It means: F'(x) = f(x). So the Fundamental Theorem makes integrating (= calculating an infinite sum of infinite small numbers  very hard!) much easier: if you can find a primitive F of f, you're done. In the case of cos(x) this is simple: (sinx)' = cos x, so F(x) = sinx.
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