Calculus
Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the xaxis.
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Anonymous

V = π∫(y^2) dx from a to b
= π∫x^4 dx from 0 to 3
= π[x^5/5] from 0 to 3
= π(243/5  0) = 243π/5 cubic unitsposted by Reiny

or, using shells, you can do
V = ∫[0,9] 2πrh dy
where r = y and h = 3x
= 2π∫[0,9] y(3√y) dy
= 2π(3/2 y^2  2/5 y^(5/2)) [0,9]
= 2π(3/2 * 81  2/5 * 243)
= 2π(243/10)
= 243π/5posted by Steve
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