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

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
y-axis.

Reiny · Answer

The line and the parabola intersect at (3,0) and (0,3)
http://www.wolframalpha.com/input/?i=plot+x%2By+%3D+3,+x+%3D+4%E2%88%92(y%E2%88%921)%5E2

from the straight line: x = 3-y

V = ?? ((4 - (y-1)^2 )^2 - (3-y)^2 ) dy from 0 to 3
= .....

I would expand first, then integrate