Solution: First we draw a picture:
This region is not of the basic type for finding an area, because its upper border is made of two graphs. Therefore, if we want to use vertical slicing and integrate with dx, we have to split it into two parts:
Now it is easy to find the area:
Note that if we use horizontal slicing, we will be able to find the area using just one integral, since the strips are of the same kind.
The integral will use dy and we have to express the endpoints of the strips (their x-coordinates) using the variable y. Another way to see this is to switch the axes and pass to inverse functions:
Thus we get
