Question

Area between curves: which function do you subtract?

So I know that the formula for finding the area between two curves is `A = int_a^b [f(x) - g(x)]dx`

But how do you determine which function should be f(x) and which should be g(x)? How do you know which is "greater?"

One other question, how do you know whether you need to be integrating with respect to x or with respect to y?

Answer 1

You subtract the curve which is below the other curve. This formular is only true if the curves do not cross within the integration-range. If that is given, you can just sub in a random value within that integration-range and get to different values. The function with the bigger value is `f(x)`. If you do not no the crossingpoints of the curves, you can find them by
`f(x)=g(x)`
The result(s) for `x` are your crossingpoints.