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

Question

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

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Answer

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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