1. Area of a Region Between Two Curves (7.1)
April 12th, 2012

2. I. Area of a Region Between Two Curves
Area of a Region Between Two Curves: If f and g are continuous on [a, b] and for all x in [a, b], then the area of the region bounded by the graphs of f and g and the vertical lines x=a and x=b is .

4. Ex 1: Find the area of the region bounded by the graphs of , ,
, and

5. You Try: Find the area of the region bounded by the graphs of , ,
, and

6. II. Area of a Region Between Two Intersecting Curves
*Calculate the upper and lower limits of the integral by determining where the two graphs intersect.

7. Ex. 2: Find the area of the region bounded by the graphs of and .

8. You Try: Find the area of the region bounded by the graphs of and.

9. *If a set of two curves intersects at more than two points, use multiple integrals to evaluate the area.

10. Ex. 3: Find the area of the region bounded by the graphs of and .

11. You Try: Find the area of the region bounded by the graphs of and.

12. *It is sometimes useful to integrate with respect to y, which means using horizontal rectangles in setting up the integral.

13. Ex. 4: Find the area of the region bounded by the graphs of f(y)=y(2-y) and g(y)=-y.

14. You Try: Find the area of the region bounded by the graphs of , g(y)=0, and y=3.