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 − 4y + 2 = y − 2.
The solutions are (2, 4) and (−1, 1). Therefore, in order to find the area of the region, we need
to evaluate the integral [(y − 2) − (y^2 − 4y + 2)] dy = [(−y2 + 5y − 4)] dy. We get [(−y^2
+ 5y − 4)] dy = = =
= .
8.
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) = 2 − y^4 and g(y) = y. First, let’s
make a sketch of the region.
