Mathematics - Definite Integration Question with Solution | TestHub

Column-IColumn-II

(A) ${\lim }_{n\to \infty }n{\int }_0^{\pi /2}(1-\sqrt[n]{\sin x})dx$ equals(P)$-\frac{\pi }{2}\ln 2$

(B) The value of definite integral ${\int }_{\infty }^0\frac{{\mathrm{ze}}^{-\mathrm{z}}}{\sqrt{1-{\mathrm{e}}^{-2\mathrm{z}}}}\mathrm{dz}$ is equal to(Q) $\frac{\pi }{2}\ln 2$

(C) The value of the definite integral ${\int }_0^{\pi }\frac{x|\sin x|}{1+|\cos x|}dx$ is equal to(R) $-\pi \ln 2$

(S) $\pi ln2$