Let . What is…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

H(x)=\displaystyle\int_{x^{2}\sin x}^{4} \sqrt{1+t}\,dt

. What is

H'\!\left(\dfrac{\pi}{2}\right)

? (a)

-\sqrt{1+\dfrac{\pi^{2}}{4}}

(b)

-\dfrac{\pi^{2}}{2}

(c)

-\pi\sqrt{1+\dfrac{\pi^{2}}{4}}

(d)

\pi\sqrt{1+\dfrac{\pi^{2}}{4}}