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 y^2 = y + 2. The
solutions are (4, 2) and (1, −1). Therefore, in order to find the area of the region, we need to
evaluate the integral (y + 2 − y^2 ) dy. We get (y + 2 − y^2 ) dy = =
− .
6. 4
We find the area of a region bounded by f(y) on the right and g(y) on the left at all points of the
interval [c, d] using the formula [f(y)− g(y)] dy. Here, f(y) = 3 − 2y^2 and g(y) = y^2.
First, let’s make a sketch of the region.
