# Thread: How to determine how many areas there are between two functions

1. ## How to determine how many areas there are between two functions

I was given a problem with two functions and two x-values for boundaries, so I found the points of intersection (there were two) and attempted to find the area between those functions, but I didn't get to finish. In any case, I would have gotten it wrong, because when graph the two functions and then look at the boundaries, there are 3 separate areas that needed to be added up. I just thought it was another problem with a parabolic curve and a line going through it, and there was only one area in between them, but it was asking me to also include the areas that were not in both functions, i.e.

Without a graphing utility and short of graphing both functions very accurately to tell this, is there any other way to see that this is what the question was asking for?

2. ## Re: How to determine how many areas there are between two functions

If the lower boundary is at x=a, the intersection points at x= b and x=c, and the upper boundary x=d, this seems to be simply $\displaystyle \int_a ^ b (f(x)-g(x))dx + \int_b^c (g(x)-f(x))dx + \int_c^d (f(x)-g(x))dx$.

Or am I missing something in your question?