Apentix/AP Calculus AB/Unit 6: Integration and Accumulation of Change/Question

AP Calculus ABhardmcq1 pt

What is the value of $\int_0^{\pi/2} \cos x\,\sin^3 x\,dx$ ?

A.

\frac{1}{2}

B.

1

C.

\frac{1}{4}

D.

-\frac{1}{4}

Explanation

Core Concept

With $u=\sin x$ , $du=\cos x\,dx$ , and the bounds become $u=0$ to $u=1$ . Then $\int_0^1 u^3\,du=\frac{1}{4}$ .

Correct Answer

C $\frac{1}{4}$

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