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Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.

x = 1 + (y − 6)^2, x = 17

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  1. The curves intersect at (17,2) and (17,10)
    v = ∫[2,10] 2πrh dy
    where r=y and h=17-x = 17-(1+(y-6)^2)
    v = ∫[2,10] 2πy(17-(1+(y-6)^2)) dy = -2π∫[2,10] (y^3-12y^2+20y) dy

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