Have a Volume by slicing and rotation about an axis question

[Zetsword]

Sry to not introduce myself and all that but kinda need help with a homework problem to get ready for a quiz this morning. The question is about volume by revolving on an axis. It's

The region in the first quadrant bounded above by the curve y = x^2, below by the x-axis, and on the right by the line x = 1, about the line x = -1. Now I've looked up the answer to be 7pi/6 but can't figure it out for the life of me. I thought that you would change the y = x^2 to sqrt(y) then find out what sqrt(y) is when the line x = 1 but it just really isn't working for me. Anybody wanna help? :|

 

[galactus]

You can use shells. With shells, the slices are parallel to the axis about which it being revolved, therefore, we integrate wrt x.

\(\displaystyle 2{\pi}\int_{0}^{1}(x+1)x^{2}dx\)

 

[Zetsword]

Thanks a lot, just got back from the quiz and a similar question was on it.