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

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.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestFirst 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.

Log in to reply

@Pi Han Goh @Kartik Sharma @Surya Prakash @Sudeep Salgia please help!

Log in to reply

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.

Log in to reply

Ooh nice :)

Log in to reply

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 !

Log in to reply

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

Log in to reply

Thanks for enlightening!

Log in to reply

There is no one :(

Log in to reply

What????

Log in to reply