1. 7.2A Volumes by Revolution: Disk/Washer Method

2. Ex 1 Find the volume of the solid obtained by rotating the region under the curve about the x-axis from 0 to 1.

3. Ex 2 Find the volume of the solid obtained by rotating the region enclosed by the curves y = x2 & y = x about
a) y –axis b) y = 2.

4. Disk:
Washer:

5. HW: 7.2A pg # 1 – 21 EOO, 23, 27, 33, 34

6. 7.3 Volumes by Revolution: Cylindrical Shell Method

7. Ex Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x2  x3 and y = 0.

8. Shell:

9. HW: 7.3 pg. 472 # 1 – 21 EOO, 27

10. Definition of Volume from a to b:

11. Ex 3 Prove that the volume of a sphere is: