How to find the new limits of integration

[firekid123]

Homework Statement

I'm confused about a certain aspect of shell method, washer method, and disk method. If I want to rotate using the washer method about the x-axis how do I get the new limits of integration?

For example: y = 9-x2 over [0,3] about x-axis.
I solved for x and got: x = sqrt(9-y) but how do I calculate the new limits?
Also do I need to find the new limits for disk, shell, and washer method in certain cases or is it only for shell and washer?

I know how to set up and solve the integral it's just calculating the new limits. Any help would be great.

 

[rock.freak667]

You are initially given values for x, so when x=0 what is y? Similarly when x=3 what is y?

(from the equation y=9-x²)

Those will be your limits.