Posted by Ryan on Wednesday, November 9, 2011 at 11:37pm.
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
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