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Question Number 110614 by mathdave last updated on 29/Aug/20

Answered by Dwaipayan Shikari last updated on 29/Aug/20

$${\int }_0^{\frac{\pi }{2}}\frac{{\left(cosx\right)}^{\pi }}{{\left(cosx\right)}^{\pi }+{\left(sinx\right)}^{\pi }}dx={\int }_0^{\frac{\pi }{2}}\frac{{\left(sinx\right)}^{\pi }}{{\left(sinx\right)}^{\pi }+{\left(cosx\right)}^{\pi }}=I$$$$2I={\int }_0^{\frac{\pi }{2}}\frac{{\left(sinx\right)}^{\pi }+{\left(cosx\right)}^{\pi }}{{\left(sinx\right)}^{\pi }+{\left(cosx\right)}^{\pi }}dx$$$$2I=\frac{\pi }{2}$$$$I=\frac{\pi }{4}$$$$$$

Commented by mnjuly1970 last updated on 29/Aug/20

$$perfect...$$

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