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# Help needed in an MCQ

$\large \displaystyle I_n \int_{\pi}^\pi \frac1{1 + 2^{\sin(x/2)} } \left( \frac{\sin(nx/2)}{\sin(x/2)} \right)^2 \, dx$

Hi brilliant! I've a doubt in calculus! The question is above.

The options are:

A) $${ I }_{ n }={ I }_{ n+1 }\forall n\ge 1$$

B) $${ I }_{ 0 },{ I }_{ 1 },{ I }_{ 2 },{ ...,I }_{ n }\quad are\quad in\quad AP$$

C) $$\sum _{ m=0 }^{ 9 }{ { I }_{ 2m }=90\pi }$$

D) $$\sum _{ m=0 }^{ 10 }{ { I }_{ m }=55\pi }$$

More than one options are right

• Please provide detail solutions!

• Please don't fluke answers.

Note by Aditya Kumar
1 year ago

## Comments

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First substitute x by -x and add to get rid of the denominator. Then use the steps in the solution of this problem. This should help you. · 1 year ago

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First substitute x by -x and add to get rid of the denominator.And then evaluate $$I_0$$,$$I_1$$,$$I_2$$.... which will come out to be $$0,\pi ,2\pi.....$$ hence they will be in AP .So B,C,D.

And that problem by Sudeep can also be evaluated like that. · 1 year ago

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Ooh nice :) · 1 year ago

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I'm sure that it's one of a, b, c or d. · 1 year ago

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Thanks for enlightening! · 1 year ago

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There is no one :( · 1 year ago

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What???? · 1 year ago

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