\( \int_{0}^{\pi} x f(\sin x) d x=k \int_{0}^{\pi / 2} f(\sin x) d x \), the value of \( k \) is....

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\( \int_{0}^{\pi} x f(\sin x) d x=k \int_{0}^{\pi / 2} f(\sin x) d x \), the value of \( k \) is
\( \mathrm{P} \)
(1) \( \frac{\pi}{2} \)
(2) \( \pi \)
(3) \( \frac{\pi}{3} \)
(4) \( 2 \pi \)
.


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