Next, we need to find where the two curves intersect, which will be the endpoints of the
region. We do this by setting the two curves equal to each other. We get x^2 − 2 = 2. The
solutions are (−2, 0) and (2, 0). Therefore, in order to find the area of the region, we need to
evaluate the integral. (2 − (x^2 − 2)) dx = (4 − x^2 ) dx. We get
(4 − x^2 ) dx = − = .
2.
We find the area of a region bounded by f(x) above and g(x) below at all points of the interval
[a, b] using the formula [f(x − g(x))] dx. Here f(x) = 4x − x^2 and g(x) = x^2.
First, let’s make a sketch of the region.
