1. 5.5 The Area of a Region Bounded by Two GraphsGoal: To calculate the area bounded by two graphs Area of a Region Bounded by Two Graphs:

2. This concept is just like what we use in geometry to find the area of a picture frame. We find the area of the outer part of the frame and subtract the area of the glass part of the picture. 2x 1_ 1_ Outer Area = 2x2 Inner area= (2x -2)(x-2) Area of “frame” = 2x2 - (2x -2)(x-2) x 1|

3. The most important thing for us to remember is to determine which function is less than the other within the given interval. That determines the order in which we subtract.

4. Find the area of the region bounded by the graphs of y = x2 + 1 and y = x for 0 ≤ x ≤ 2. Sketch the region bounded by the graphs.

5. Find the area of the region bounded by the graphs of y = 3 – x2 and y = 2x.

6. Find the area of the region bounded by the graphs of y = x2 –x - 2 and the x-axis.

7. Find the area of the region bounded by the graphs of ƒ(x)= x3 +2x2 – 3x and g(x)= x2 + 3x. Sketch a graph of the region.