Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y = 3, x = 4−(y−1)^2; about the x-axis.

Answer 1

The intersection between the curves are
3, 0
0, 3
The volume of the solids is obtained by
V = ∫ π [ (4 - (y-1)²)² - (3 - y)²] dy with limits from 0 to 3
The volume is
V = 108π/5 or 67.86