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I am trying to solve the following definite integral;

$\int_0^\pi (\sin x )^{\cos x} dx$?

amWhy
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Albert
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  • @OmG Your input is wrong. You computed the integral of the function $x\cdot \sin(x)^{\cos(x)}$ instead of $\sin(x)^{\cos(x)}$. It does not alter the fact that it does not converge but I would say it is important to be precise concerning the integrand. – mrtaurho Dec 08 '18 at 13:51

1 Answers1

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The integral does not exist, because $\sin(\pi-\epsilon) = \epsilon + o(\epsilon^3)$ and $\cos(\pi-\epsilon) = -1 + \epsilon^2/2 + o(\epsilon^3),$ i.e. the integrand has a pole at $x=\pi.$

gammatester
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