# Shell Method

1. Dec 6, 2009

### gwoody_wpcc

1. The problem statement, all variables and given/known data

Have to find the volume using the shell method using the given curves

x=3y-y^2 and the y-axis about the x-axis

2. Relevant equations
I know to use the equation V=2pi Integral y f(y) dy but no idea where to get the high and low limits for the integral

3. The attempt at a solution

Last edited: Dec 6, 2009
2. Dec 6, 2009

### Staff: Mentor

Have you graphed the equation x = 3y - y^2? Its graph is a paraboloa that opens to the left. You can find the vertex of the parabola by completing the square in the y terms.

Your typical volume element is $\Delta V = 2\pi*y*x*\Delta y$. Since you will be integrating with respect to y, you need to replace x in this formula with 3y - y^2. From the graph you can also get the limits of integration.