calculus
posted by Ryan on .
Find the volume of the solid generated by revolving about line x = 4 the region bounded by x = y  y^2 and x = y^2  3

The curves intersect at (2,1) and (3/4,3/2)
So, we want to sum up the washers with inner radius r and outer radius R
Int pi*(R^2  r^2)[1,3/2] dy
where
R = y  y^2 + 4
r = y^2  3 + 4 = y^2 + 1
R^2  r^2
= (y^2  y^3 + 4y  y^3 + y^4  4y^2 + 4y  4y^2 + 16)  (y^4 + 2y^2 + 1)
= 2y^3  9y^2 + 8y + 15
V = pi*(1/2 y^4  3y^3 + 4y^2 + 15y)[1,3/2]
= 1085pi/96