1. Area Between Two Curves 7.1

2. Area Formula If f and g are continuous functions on the interval [a, b], and if f(x) > g(x) for all x in [a, b], then the area of the region bounded above by y = f(x), below by y = g(x), on the left by x = a and on the right by x = b is….

3. Area between two curves (Graph)

4. Example 1 Find the area of the region bounded above by y = x + 6 and below by y = x², and bounded on the sides by the lines x = 0 and x = 2.

5. Example 1 Find the area of the region bounded above by y = x + 6 and below by y = x², and bounded on the sides by the lines x = 0 and x = 2.

6. Example 2 Find the area of the region that is enclosed between the curves y = x² and y = x + 6

7. Example 2 Find the area of the region that is enclosed between the curves y = x² and y = x + 6

8. Example 3 Find the area enclosed by the curves and

9. Example 3 Find the area enclosed by the curves and

10. Practice Sketch the region enclosed by and then find the area.

11. Practice Sketch the region enclosed by and then find the area.

12. Example 4 Find the area of the region that is enclosed between the curves x = y² and y = x – 2 What’s different about this question?

13. Example 4 Find the area of the region that is enclosed between the curves x = y² and y = x – 2 What’s different about this question?

14. Two ways to solve….. #1 Subdivide the regions Equation of top graph – equation of bottom graph Equations must be solved in terms of y and bound are determined by x values

15. #2 Reverse the roles of x and y – When reversing roles you always subtract the graph on the right – graph on left – Must solve equations in terms of x and gets bounds in terms of y

16. Example 5 Find the area of the region enclosed by the curves and x = 1.

17. Example 6 Find the area of the region enclosed by the curves and

18. Practice Pg. 448 (1 – 23 odd)