\[\int_{0}^{\pi }{x}\,f\,(\sin x)\,dx=\] [IIT 1982; Kurukshetra CEE 1993]

\[\frac{\pi }{2}\int_{0}^{\pi /2}{f(\sin x)\,dx}\]

\[\pi \int_{0}^{\pi }{f(\sin x)\,dx}\]

\[\frac{\pi }{2}\int_{0}^{\pi }{f(\sin x)\,dx}\]

\[\int_{0}^{\pi }{x}\,f\,(\sin x)\,dx=\] [IIT 1982; Kurukshetr

1.	\[\int_{0}^{\pi }{x}\,f\,(\sin x)\,dx=\] [IIT 1982; Kurukshetra CEE 1993]
A.	\[\pi \int_{0}^{\pi }{f(\sin x)\,dx}\]
B.	\[\frac{\pi }{2}\int_{0}^{\pi }{f(\sin x)\,dx}\]
C.	\[\frac{\pi }{2}\int_{0}^{\pi /2}{f(\sin x)\,dx}\]
D.	None of these
Answer» C. \[\frac{\pi }{2}\int_{0}^{\pi /2}{f(\sin x)\,dx}\]

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\[\int_{0}^{\pi }{x}\,f\,(\sin x)\,dx=\] [IIT 1982; Kurukshetra CEE 1993]

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