What is the area between two curves?

The area between two curves is the integral of the absolute difference of the two functions defining the curves over the interval where they intersect. Here are the steps to find it:

1. Identify the two curves and the interval where they intersect. The curves are usually given as functions, like f(x) and g(x). The intersection points can be found by setting the two functions equal to each other and solving for x.

2. Determine which curve is above the other in the interval. This can be done by picking a point in the interval (not an endpoint) and plugging it into both functions. The function with the higher value is the upper curve.

3. Set up the integral from the lower limit to the upper limit of the absolute difference of the two functions. This is usually written as ∫ from a to b of |f(x) - g(x)| dx, where a and b are the endpoints of the interval.

4. Evaluate the integral. This will give you the area between the two curves.

Remember, the area should always be a positive number. If you get a negative number, it means you have the upper and lower curves switched.