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How can I calculate $\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}dt$?
How can we integrate $$\int_0^\frac{\pi}2\frac{\sin^nx}{\sin^nx+\cos^nx}dx , \,\,\,\,\,\,\,\,\, n\in N \quad?$$ Thanks for any hint.
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marked as duplicate by Amzoti, Brett Frankel, Micah, TMM, Thomas Feb 1 at 21:50
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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Hint: Make the change of variable $u=\frac{\pi}{2} -x$, noting that $\sin\left(\frac{\pi}{2}-x\right)=\cos x$. Then replace the letter $u$ by $x$, and the answer will hit you. Remark: The hint is given in the language of formal manipulations, but the idea is purely geometric. |
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