Determine the exact value of .

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

Problem

Determine the exact value of

\displaystyle \int_{0}^{\pi} x^{3}\cos x\,dx

. (a)

3\pi^{2}

(b)

6-3\pi^{2}

(c)

12-3\pi^{2}

(d)

-6-3\pi^{2}