Mathematics - Definite Integration Question with Solution | TestHub

$$\begin{array}{rlr}& =0-2\underset{x\to 0^{+}}{\mathrm{Lt}}x\ln \sin x-2\frac{\pi }{2}\ln \frac{1}{2}=\pi \ln 2& \left(\because \underset{x\to 0^{+}}{\mathrm{Lt}}\frac{\ln \sin x}{1/x}=\underset{x\to 0^{+}}{\mathrm{Lt}}\frac{\frac{1}{\sin x}\cdot \cos x}{-\frac{1}{x^2}}=0\right)\end{array}$$