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Definite Integration question

2009 · Shift 2 · Q25

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2009 · Shift 2 · Q25

Definite Integration question

2009 · Shift 2 · Q25

JEE AdvancedMathematicsDefinite IntegrationMultiple correct+4 / −2

If

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

.... then

A
${I_n} = {I_{n + 2}}$
B
$\sum\limits_{m = 1}^{10} {{I_{2m + 1}}} = 10\pi$
C
$\sum\limits_{m = 1}^{10} {{I_{2m}}} = 0$
D
${I_n} = {I_{n + 1}}$

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