Apentix/AP Calculus AB/Unit 8: Applications of Integration/Question

AP Calculus ABeasymcq1 pt

The region bounded by the graph of $y=x^2$ , the $x$ -axis, and the line $x=2$ is revolved about the $x$ -axis. What is the volume of the resulting solid?

A.

\frac{8\pi}{3}

B.

2\pi

C.

32\pi

D.

\frac{32\pi}{5}

Explanation

Core Concept

Each cross-section is a disc of radius $x^2$ , so $V=\pi\int_0^2 x^4\,dx=\pi[\frac{x^5}{5}]_0^2=\frac{32\pi}{5}$ .

Correct Answer

D $\frac{32\pi}{5}$

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