Shell Method Help - 24pi(-2/5y^2+7/5y^3-y^4)dy

[dakar76]

Homework Statement

X=12(y^2-y^3) Rotation is around y=-2/5

Homework Equations

V=2pi from the integral of a to b (shellradius)(shell height) dx

The Attempt at a Solution

2pi (-2/5+y)(12)(y^2-Y^3)dy
24pi (-2/5+y)(y^2-y^3)dy
24pi (-2/5y^2+7/5y^3-y^4)dy
24pi (-8/60y^2+21/60y^4-12/60y^5)
answer i get is 2/5pi when i integrat from 0 to 1 the book answer is 2pi

 

[Mark44]

Please post the entire problem statement. Is the region being rotated bounded by some line, such as the y-axis?