How do you find the volume of a solid of revolution using integration?

[pugtm]

Homework Statement

x=2y^2
x=0
y=+-6
rotated around y

Homework Equations

integral 2pi*x(f(x)dx

The Attempt at a Solution

integral from -6 to 6 of 2pi*y*2y^2 dy
but i get something far less than the correct answer

 

[QuarkCharmer]

What are all the * symbols supposed to mean? Multiplication?

Just think of this as Area times length. Since it's rotation around the y-axis you can see that it's easiest to differentiate with respect to y. It's going to make a bunch of little circles. What is the radius of those? (your function?).

From there, you need to plug it into the area of a circle to get pi(radius)^2
So if the volume of the solid is area times width, and in the integration dy is the width, what integral would solve this problem?