Determine the value of ∫0π/2ln(sinx)dx\int_0^{\pi/2} \ln(\sin x) dx∫0π/2ln(sinx)dx.
−π2ln2-\frac{\pi}{2} \ln 2−2πln2
000
πln2\pi \ln 2πln2
−πln2-\pi \ln 2−πln2