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Evaluate: int(pi//4)^(pi//2)cos2xlogsinx...

Evaluate: `int_(pi//4)^(pi//2)cos2xlogsinxdx`

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To evaluate the integral \( I = \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cos(2x) \log(\sin x) \, dx \), we will use integration by parts. ### Step 1: Identify \( u \) and \( dv \) Let: - \( u = \log(\sin x) \) - \( dv = \cos(2x) \, dx \) ### Step 2: Differentiate \( u \) and integrate \( dv \) ...
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