Volumes by Disk and Washer Methods

AP Calculus AB· difficulty 3/5

The washer method for a region between y=f(x)y = f(x) (outer) and y=g(x)y = g(x) (inner), revolved about the xx-axis, gives volume

  • A

    πabfgdx\pi\int_a^b f g\,dx

  • B

    ab2π(fg)dx\int_a^b 2\pi(f - g)\,dx

  • C

    πab(fg)2dx\pi\int_a^b (f - g)^2\,dx

  • D

    πab(f2g2)dx\pi\int_a^b (f^2 - g^2)\,dx

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Explanation

Outer disk minus inner disk: π(f2g2)\pi(f^2 - g^2).

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