AP calc

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y = 8x − x^2, y = 12; about x = 2

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  1. each shell has volume

    2πrh dx where
    r = x-2
    h = y

    so,

    v = ∫[2,6]2π(x-2)(8x-x^2) dx

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