Let and define

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

Let

g(t)=\begin{cases}t^{2}, & t\le 0,\\2t, & t>0,\end{cases}

and define

p(x)=\displaystyle\int_{x}^{\sin x} g(t)\,dt

. Given that

g(0)=0

, what is

p'(0)

? (a)

2

(b)

-2

(c)

0

(d)

p'(0)\text{ is undefined}