Volumes by Disk and Washer Methods

AP Calculus AB· difficulty 3/5

Rotate x=y2x = y^2, 0y20 \le y \le 2, about the yy-axis. Volume by disks (in yy):

  • A

    π02y2dy=8π3\pi\int_0^2 y^2\,dy = \dfrac{8\pi}{3}

  • B

    02y4dy\int_0^2 y^4\,dy

  • C

    2π02y2dy2\pi\int_0^2 y^2\,dy

  • D

    π02y4dy=32π5\pi\int_0^2 y^4\,dy = \dfrac{32\pi}{5}

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Explanation

Disks of radius x=y2x = y^2, thickness dydy: πy4dy\pi y^4\,dy.

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