Prove that .

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

Prove that ∫0πxf(sin⁡x)dx=π2∫0πf(sin⁡x)dx\int_{0}^{\pi} x f(\sin x) dx = \frac{\pi}{2} \int_{0}^{\pi} f(\sin x) dx .

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