The value of $\int\limits_{-\pi / 2}^{\pi / 2}\left(p \sin ^3 x+q \sin ^4 x+r \sin ^5 x\right) d x$ depends on:
Answer & explanation
Correct answer: option 2
$I=\int\limits_{-\pi / 2}^{\pi / 2}\left(p \sin ^3 x+q \sin ^4 x+r \sin ^5 x\right) d x$
$=q \int\limits_{-\pi / 2}^{\pi / 2} \sin ^4 x dx = q $
(Since sin3x and sin5x are odd functions)
Hence (2) is the correct answer.