Find the exact value of .

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

Problem

Find the exact value of

\displaystyle\int_{0}^{\pi} \frac{\sin(\sqrt{x})}{\sqrt{x}}\,dx

. (a)

2\bigl(1+\cos\sqrt{\pi}\bigr)

(b)

2\bigl(1-\cos\sqrt{\pi}\bigr)

(c)

1-\cos\sqrt{\pi}

(d)

2\bigl(1-\cos \pi\bigr)