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- Thread starter akbarali
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For the second one, the derivative form of the FTOC gives us:

If:

\(\displaystyle G(x)=\int_a^x f(t)\,dt\)

then:

\(\displaystyle G'(x)=f(x)\)

You have cited a more general case, but can you see that you have added something to your result which should not be there?

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\(\displaystyle \int_0^{\pi}\sin(x)\,dx=-\left[\cos(x) \right]_0^{\pi}=-\left(\cos(\pi)-\cos(0) \right)=-(-1-1)=-(-2)=2\)

For the second problem, I would simply write:

\(\displaystyle \frac{d}{dx}\left(\int_0^x e^{\sin(s)+s^s}\,ds \right)=e^{\sin(x)+x^x}\)

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