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18 August, 10:09

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 64x-8x^2, y = 0; about the y-axis.

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  1. 18 August, 10:14
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    We need to get the limits first. When y = 0

    0 = 64x - 8x^2

    x = 0 and x = 8

    The volume is

    V = ∫ y dx from 0 to 8

    V = ∫ (64x - 8x^2) dx from 0 to 8

    V = 32x^2 - 8x^3/3 from 0 to 8

    V = 682.67
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