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The value f the integral int(-pi)^pisinm...

The value f the integral `int_(-pi)^pisinm xsinn xdx ,` for `m!=n(m , n in I),i s` 0 (b) `pi` (c) `pi/2` (d) `2pi`

A

`0`

B

`pi`

C

`pi//2`

D

`2pi`

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(-pi)^(pi) sin n x sin mx dx=int_(0)^(x) 2 sin mx sin nx dx`
`=int_(0)^(pi) [cos(m-n)xcos(m+n)x]dx`
`=|(sin(m-n)x)/(m-n)-(sin(m+n)x)/(m+n)|_(0)^(pi)=0`
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