Finding Volume Using Shell Method: x=3y-y^2

[gwoody_wpcc]

Homework Statement

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

Homework 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

The Attempt at a Solution

 

[Mark44]

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.