IIT-JEE 2009 Paper 2 Offline | Definite Integration Question 43 | Mathematics

IIT-JEE 2009 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

If $${I_n} = \int\limits_{ - \pi }^\pi {{{\sin nx} \over {(1 + {\pi ^x})\sin x}}dx,n = 0,1,2,} $$ .... then

$${I_n} = {I_{n + 2}}$$

$$\sum\limits_{m = 1}^{10} {{I_{2m + 1}}} = 10\pi $$

$$\sum\limits_{m = 1}^{10} {{I_{2m}}} = 0$$

$${I_n} = {I_{n + 1}}$$

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