From x = −3 to x = 0, if you slice the region vertically, the curve y = is on top, and the x-axis is
on the bottom; from x = 0 to x = 3, the curve y = is on top and the x-axis is on the bottom.
Therefore, you can find the area by evaluating two integrals.
( − 0) dx and ( − 0) dxYour results should be
Let’s suppose you sliced the region horizontally instead. The curve y = is always on the left, and
the curve y = is always on the right. If you solve each equation for x in terms of y, you save some
time by using only one integral instead of two.
The two equations are x = y^2 − 3 and x = 3 − y^2 . We also have to change the limits of integration from x-