1. Sec 6.1: AREAS BETWEEN CURVES
Area between two curves

2. Sec 6.1: AREAS BETWEEN CURVES
Area between two curves
Example:
Find the area of the region bounded by the curves
and
Note:
Both right-hand and left-hand boundary are lines

3. Sec 6.1: AREAS BETWEEN CURVES
Area between two curves
Note:
Both right-hand and left-hand boundary reduce to a point

4. 1) Find the intersection points
Sec 6.1: AREAS BETWEEN CURVES
Area between two curves
Note:
The value of a and b (not given)
Steps:
1) Find the intersection points
2) Write the area as an integral

5. Sec 6.1: AREAS BETWEEN CURVES
Area between two curves

6. Sec 5.5: THE SUBSTITUTION RULE

7. Sec 5.5: THE SUBSTITUTION RULE

8. Sec 6.1: AREAS BETWEEN CURVES

9. Sec 6.1: AREAS BETWEEN CURVES
Area between two curves
Some regions are best treated by regarding x as a function of y.

10. Sec 6.1: AREAS BETWEEN CURVES
Area between two curves
Some regions are best treated by regarding x as a function of y.

11. 1) Rewrite the function as x in terms of y
Sec 6.1: AREAS BETWEEN CURVES
Steps:
1) Rewrite the function as x in terms of y
2) Find the intersection points

12. Sec 6.1: AREAS BETWEEN CURVES
We could have found the area in by integrating with respect to x instead of y, but the calculation is much more involved.

13. Sec 6.1: AREAS BETWEEN CURVES

14. Sec 6.1: AREAS BETWEEN CURVES