INTEGRATION (IIT 2009)

If I_{n}=\int_{-\pi }^{\pi }{\frac{sin (nx)}{(1 + \pi ^{x})sin x}}dx, n = 0,1,2.... then

A) I_{n} = I_{n+2} B) \sum_{m=1}^{10}{I_{2m+1}} = 10\pi C) \sum_{m=1}^{10}{I_{2m}} = 0 D) I_{n} = I_{n+1}

(MULTIPLE OPTIONS CORRECT)

2 Answers

they main trick here is see what is I(x)+I(-x)

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