Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 64x−8x^2, y = 0; about the y-axis.

Answer 1

We need to get the limits first. When y = 0
0 = 64x - 8x^2
x = 0 and x = 8
The volume is
V = ∫ y dx from 0 to 8
V = ∫ (64x - 8x^2) dx from 0 to 8
V = 32x^2 - 8x^3/3 from 0 to 8
V = 682.67<span />