Area Between Two Curves

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)