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Volumes by Disk and Washer Methods

AP Calculus AB· difficulty 3/5

Region bounded by y=1y = 1, y=exy = e^x, and x=1x = 1 revolved about the xx-axis:

  • A

    π(e2+1)/2\pi(e^2 + 1)/2

  • B

    πe2\pi e^2

  • C

    π(e2−1)/2\pi(e^2 - 1)/2

  • D

    π(e2−3)/2\pi(e^2 - 3)/2

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Explanation

Washer: outer exe^x, inner 11. V=π∫01(e2x−1) dx=π(e2/2−1/2−1)=π(e2−3)/2V = \pi\int_0^1 (e^{2x} - 1)\,dx = \pi(e^2/2 - 1/2 - 1) = \pi(e^2 - 3)/2.

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