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 − 4x − 5 = 2x − 5.
The solutions are (0, −5) and (6, 7). Therefore, in order to find the area of the region, we need
to evaluate the integral. [(2x − 5) − (x^2 − 4x − 5)] dx = (−x^2 + 6x) dx. We get (−x^2 +
6 x) dx = = − 0 = 36.
4.
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.
First, let’s make a sketch of the region.
