Could you provide a specific example? Area must be a positive quantity - always.
Well, it might be more complicated than that. Let me give you an example, and see how you do. Find the area enclosed between the two curves and from to
Here's a plot (which, incidentally, I would always start out by doing. It gives a great overview of the kind of thing you need to do.)
How would you start?
[EDIT]: Fixed link. Thanks to NOX Andrew.
Your link is broken for me. In case it is also broken for hunt798, here is the link to the plot again: http://www.wolframalpha.com/input/?i=Plot[{x^2,2-x^2},{x,-2,2}]
Sounds to me like you are mixing up which curve is above the other.
For example, if I were asked to determine the area between the curves and , the first thing I would is draw (or at least visualize) the graphs, noting that they intersect when so that . That is they intersect at (-1, 1) and (2, 4). I would also recognize that the graph of is always below the graph of y= x+ 2 so the area between them is given by
Had I mistakenly written the integral as
(perhaps just because I am used to writing polynomials with highest power first!)
I would get .