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ZeHanz Group TitleBest ResponseYou've already chosen the best response.0
Do you know the Fundamental Theorem of Calculus?
 one year ago

Shadowys Group TitleBest ResponseYou've already chosen the best response.0
note that \(\int cos x dx= sin x +C\)
 one year ago

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

ZeHanz Group TitleBest ResponseYou've already chosen the best response.0
F 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.
 one year ago
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