Example 2: Area of a Region Bounded by Two Curves

Find the area of the region bounded above by y = x + 2 and below by y = x².

Part of the problem is to find the limits of integration. First draw a sketch (Figure 4.5.5). The curves intersect at two points, which can be found by solving the equation x + 2 = x² for x.

x² - (x + 2) = 0,(x + 1)(x - 2) = 0,

x = - 1 and x = 2.

Then

Figure 4.5.5