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 2 − y^4 = . The
solutions are (1, 1) and (1, −1). Therefore, in order to find the area of the region, we need to
evaluate the integral dy. We get dy =
= = = .
SOLUTIONS TO PRACTICE PROBLEM SET 25
- 36 π
When the region we are revolving is defined between a curve f(x) and the x-axis, we can find
the volume using disks. We use the formula V = π [f(x)]^2 dx. Here we have a region between
