Prove that _ 0 ^ /2 ( x) dx = _ 0 ^ /2 ( x) dx = - 2 2

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

Prove that ∫0π/2log⁡(sin⁡x)dx=∫0π/2log⁡(cos⁡x)dx=−π2log⁡2\int_{0}^{\pi/2} \log (\sin x) dx = \int_{0}^{\pi/2} \log (\cos x) dx = -\frac{\pi}{2} \log 2

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