Match the following : | Column I | Column II | |---|---| |

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

Match the following :

Column I	Column II
(A) If $I = \int \frac{\sin x - \cos x}{\sin x - \cos x}\,dx$ , where $\frac{\pi}{4} < x < \frac{3\pi}{8}$ , then $I$ is equal to	(p) $\sin x$
(B) If $\int \frac{x^2}{(x^3 + 1)(x^3 + 2)}\,dx = \frac{1}{3} f\left(\frac{x^3 + 1}{x^3 + 2}\right) + C$ , then $f(x)$ is equal to	(q) $x + C$
(C) If $\int \sin^{-1} x \cdot \cos^{-1} x\,dx = f^{-1}(x)\left[\frac{\pi}{2} x - x f^{-1}(x) - 2\sqrt{1-x^2}\right] + 2x + C$ , then $f(x)$ is equal to	(r) $\ln x$
(D) If $\int \frac{dx}{x f(x)} = f(f(x)) + C$ , then $f(x)$ is equal to	(s) $\sin^{-1} x$