Let R be the region shown below. Write an integral expression for the area of R, using horizontal slices.
We need to split R at y = 1, since the graphs of and y = 5 – x2 cross each other at this point. We get two new regions:
We found an integral expression for each of these areas, using horizontal slices, earlier. The area of the lower region is
and the area of the upper region is
Adding these, we find the area of R to be