(a) Evaluate $\int\limits_{0}^{\pi} \frac{xdx}{1 + \sin x}$. (b) Define gamma and beta functions. Prove that $\Gamma\left(\frac{1}{2}\right) = \sqrt{\pi}$.

(a) Evaluate $\int\limits_{0}^{\pi} \frac{xdx}{1 + \sin x}$. (b) Defi…

Previous year question with solution for Engineering Mathematics-I.