If there is an area between 2 curves and it's spun around the x-axis I integrate with respect to x, else if it's spun around the y-axis I integrate with respect to y. What screws me up is finding the area because I subtract the wrong function. For example, and . The is on top but the is to the right.

Which rule takes precedence; right-left or top-bottom?

If I get a negative volume, chances are I have the functions switched around, but the converse isn't always true right? For example I could still have the the functions switched around and still get a positive answer?