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

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

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

4. Sec 6.1: AREAS BETWEEN CURVES
No end points [a, b]
First, find the intersection points
Area between two curves

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

6. T-092 Sec 5.5: THE SUBSTITUTION RULE Find intersection points Graph
Write as an integrals
T-092

7. Sec 5.5: THE SUBSTITUTION RULE

8. Sec 5.5: THE SUBSTITUTION RULE
Integrating with respect to y
T-121

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

10. Sec 6.1: AREAS BETWEEN CURVES
Integrating with respect to y
Rewrite functions as x=f(y)
Find the end points y=c,y=d
Identify xR and xL

11. Sec 5.5: THE SUBSTITUTION RULE

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. T-092 Sec 6.1: AREAS BETWEEN CURVES
Note: Make sure you identify the region before you start integration.
T-092

15. Sec 5.5: THE SUBSTITUTION RULE