Evaluate ∫0π/2ln(sinx) dx\int_{0}^{\pi/2} \ln(\sin x) \, dx∫0π/2ln(sinx)dx using the property 2I=∫0π/2ln(sinx)dx+∫0π/2ln(cosx)dx2I = \int_0^{\pi/2} \ln(\sin x) dx + \int_0^{\pi/2} \ln(\cos x) dx2I=∫0π/2ln(sinx)dx+∫0π/2ln(cosx)dx.
−π2ln2-\frac{\pi}{2} \ln 2−2πln2
π2ln2\frac{\pi}{2} \ln 22πln2
−πln2-\pi \ln 2−πln2
πln2\pi \ln 2πln2