MCQ
The value of definite integral $\int\limits_\infty ^0 {\frac{{z\,{e^{ - z}}}}{{\sqrt {1 - {e^{ - 2z}}} }}\,dz} $.
- ✓$-\frac{\pi }{2}\,\ln 2$
- B$\frac{\pi }{2}\,\ln 2$
- C$- \pi\, ln\, 2$
- D$\pi \,ln\, 2$
$l=-\int_{0}^{\pi / 2} \frac{\ln (\sin \theta)(-\cos \theta) d \theta}{\sqrt{1-\sin ^{2} \theta}}=\int_{0}^{\pi / 2} \ln \sin \theta d \theta$
$\frac{-\pi}{2} \ln 2$
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