_ - a ^a x ,f( x) ,dx = - Vidyadip

MCQ

$\int_{ - a}^a {\sin x\,f(\cos x)\,dx = } $

A
$2\int_0^a {\sin x\,f(\cos x)\,dx} $
✓
$0$
C
$1$
D
None of these

✓

Answer

Correct option: B.

$0$

b
(b) $I = \int_{ - a}^a {\sin xf(\cos x)\,dx} $

$f(x) = \sin x\,f(\cos x) \Rightarrow f( - x) = - \sin x\,f(\cos x)$

$\because \,\,\,\,f(x)$ is an odd function

$\therefore \,\,\,I = \int_{}^{} {f(x)dx = 0} $.

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