Cross-sections perpendicular to x-axis are semicircles with diameter f(x). Volume equals:

\dfrac{\pi}{8} \inta^b [f(x)]^2\,dx Semicircle area = \tfrac12 \pi r^2 with r = f(x)/2, giving \tfrac{\pi}{8} f(x)^2.

\dfrac{\pi}{2} \inta^b f(x)\,dx

\dfrac{\pi}{8} \inta^b [f(x)]^2\,dx

Volumes by Disk and Washer Methods

AP Calculus AB· difficulty 4/5

x

Explanation

= \tfrac12 \pi r^2

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