The value of the integral \( \int_{0}^{\pi} x \log \sin x d x \), is (A) \( \frac{\pi}{2} \log 2...

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The value of the integral
\( \int_{0}^{\pi} x \log \sin x d x \), is
(A) \( \frac{\pi}{2} \log 2 \)
(B) \( \frac{\pi^{2}}{2} \log 2 \)
(C) \( -\frac{\pi^{2}}{2} \log 2 \)
(D) none of these
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