Mathematics

Problem

Match the following.

Column I	Column II
(A) If $f(x) = \int_{0}^{s(x)} \frac{dt}{\sqrt{1+t^3}}$ , where $g(x) = \int_{0}^{\cos x} (1 + \sin t^2) dt$ , then value of $f'\left(\frac{\pi}{2}\right)$ is	(p) $-2$
(B) If $f(x)$ is a non-zero differentiable function such that $\int_{0}^{x} f(t) dt = \{f(x)\} ^2$ , $\forall x \in \mathbb{R}$ , then $f(2)$ is equal to	(q) 2
(C) If $\int_{a}^{b} (2 + x - x^2) dx$ is maximum, then $a + b$ is equal to	(r) 1
(D) If $\lim_{x \to 0} \left( \frac{\sin 2x}{x^3} + a + \frac{b}{x^2} \right) = 0$ , then $3a + b$ has the value	(s) $-1$