AP

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

Problem

Compute

\displaystyle \int_{0}^{\pi/4} \theta^{3}\sin\!\left(\theta^{2}\right)\,d\theta

. (a)

\displaystyle \tfrac12\bigl[\tfrac{\pi^{2}}{16}\cos(\tfrac{\pi^{2}}{16})+\sin(\tfrac{\pi^{2}}{16})\bigr]

(b)

\displaystyle \tfrac12\bigl[-\tfrac{\pi^{2}}{16}\cos(\tfrac{\pi^{2}}{16})+\sin(\tfrac{\pi^{2}}{16})\bigr]

(c)

\displaystyle \tfrac12\bigl[-\tfrac{\pi}{4}\cos(\tfrac{\pi}{4})+\sin(\tfrac{\pi}{4})\bigr]

(d)

\displaystyle -\tfrac{\pi^{2}}{16}\cos(\tfrac{\pi^{2}}{16})+\sin(\tfrac{\pi^{2}}{16})