# 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

5 years, 8 months ago

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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.

- 5 years, 8 months ago

- 5 years, 8 months ago

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.

- 5 years, 7 months ago

Ooh nice :)

- 5 years, 7 months ago

i think you have written the statement wrong it should be -pi to pi , correct it then only answers can be given @Aditya Kumar if it's -pi to pi then the answer would be B,C,D .....just correct it !

- 4 years, 7 months ago

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

- 5 years, 8 months ago

Thanks for enlightening!

- 5 years, 8 months ago

There is no one :(

- 5 years, 8 months ago

What????

- 5 years, 8 months ago