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 = 13 sqr.(x)
y = 0, x = 1; about x = −3

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  1. the volume of a shell of radius r, height h and thickness dr is

    v = 2πrh dr

    So, add up your shells, where
    r = x+3 = (y/13)^2
    h = y

    v = ∫[0,2] 2π ((y/13)^2+3) y dy = 2036π/169

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  2. oops. the shells have thickness dx.

    v = ∫[0,2] 2π (x+2)(13√x)dx = 1644√2/15 π

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