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Volumes by Disk and Washer Methods

AP Calculus AB· difficulty 3/5

Region between y=4y = 4 and y=x2y = x^2 revolved about the xx-axis on [0,2][0, 2]:

  • A

    64π5\tfrac{64\pi}{5}

  • B

    16π5\dfrac{16\pi}{5}

  • C

    96π5\tfrac{96\pi}{5}

  • D

    128π5\tfrac{128\pi}{5}

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Explanation

Washer: outer y=4y = 4, inner y=x2y = x^2. V=π∫02(16−x4) dx=π(32−32/5)=128π/5V = \pi\int_0^2 (16 - x^4)\,dx = \pi(32 - 32/5) = 128\pi/5.

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