TITLE: Area between two curves, which curve is on top?
QUESTION [5 upvotes]: Given a question like this:
Find the area between ${y = x^2 + 2x - 3}$ and ${y = 2x^2 -5x  -3}$.
I know how to find the area ${\int y_1 - y_2}$ but how can I tell which one is the top curve?  Are there any shortcuts to determining the top curve?

REPLY [3 votes]: Assuming you work only with polynomials and they don't intersect here is a little shortcut: 
Find the highest exponent, that is different for both polynomials. The one, with the higher coefficient is on top.