1. Volume: The Disk Method
Section 7.2
Volume: The Disk Method

2. Examples (from mathdemos.org)

3. Examples (from mathdemos.org)

4. Examples (from mathdemos.org)

5. Examples (from mathdemos.org)

6. Examples (from mathdemos.org)

7. Formulas: Disk Method (about x axis)
Note: Function must be of the form:
y = _____
and a and b are in terms of x values

8. Formulas: Disk Method (about y axis)
Note: Function must be of the form:
x = _____
and c and d are in terms of y values

9. Formulas: Washer Method (about x axis)
Note: Function must be of the form:
y = _____
and a and b are in terms of x values

10. Formulas: Washer Method (about y axis)
Note: Function must be of the form:
x = _____
and c and d are in terms of y values

11. Washer Method Revolving about a Line
R(x) = Line - Farthest Graph
r(x) = Line - Nearest Graph

12. 1. Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis (similar to p.465 #1-5)

13. 2. Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis (similar to p.465 #1-5)

14. 3. Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis (similar to p.465 #7-9)

15. 4. Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis (similar to p.465 #7-9)

16. the x-axis the y-axis the line x = 8 the line x = 10
5. Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines (similar to p.465 #11-13)
the x-axis
the y-axis
the line x = 8
the line x = 10

17. 6. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 6 (similar to p.465 #15-17)

18. 7. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5 (similar to p.465 #19-21)

19. 8. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis (similar to p.465 #23-29)

20. 9. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis (similar to p.465 #33-35)