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# The value of $\int\limits_{0}^{\pi/2}\large\frac{\cos^{5/3}x}{\cos^{5/3}x+\sin^{5/3}x}$$dx is $\begin{array}{1 1}(1)\frac{\pi}{2}&(2)\frac{\pi}{4}\\(3)0&(4)\pi\end{array}$ Can you answer this question? ## 1 Answer 0 votes \int\limits_{0}^{\pi/2}\large\frac{\cos^{5/3}x}{\cos^{5/3}x+\sin^{5/3}x}=\frac{1}{2} \int \limits_0 ^{\pi/2}$$dx$
$\qquad= \large\frac{1}{2} [ \frac{1}{2} -0]$
$\qquad= \large\frac{\pi}{4}$
Hence 2 is the correct answer.
edited May 20, 2014 by meena.p