Volumes by Disk and Washer Methods

AP Calculus AB· difficulty 4/5

The region bounded by y=xy = \sqrt{x}, y=0y = 0, x=4x = 4 is rotated about the x-axis. The volume is

  • A

    32π3\frac{32\pi}{3}

  • B

    8π8\pi

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  • C

    4π4\pi

  • D

    16π16\pi

Explanation

Disks: V=π04xdx=π[x2/2]04=8πV = \pi \int_0^4 x\,dx = \pi[x^2/2]_0^4 = 8\pi.

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