Question

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`

Answer 1

Correct Answer - 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`