The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.
x = (y − 6)^2, x = 1; about y = 5
using shells of thickness dy,
∫[5,7] 2πrh dy
where r = y-5 and h = 1-x
∫[5,7] 2π(y-5)(y-6)^2 dy
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