1. Ms. Yoakum Calculus

2. Click one:

3. Disk Method Cylindrical Shells Method Washer Method Back Click one:

4. Next

5. Volume = R Next

6. Determine the volume of the solid obtained by rotating the region bounded by,,, and the x-axis about the x-axis. Problem courtesy of: http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx Next

7. r Volume = Determine the volume of the solid obtained by rotating the region bounded by,,, and the x-axis about the x-axis. Problem courtesy of: http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx Done

8. Next

9. (Horizontal Axis of Revolution) r Volume = Next

10. Determine the volume of the solid obtained by rotating the portion of the region bounded by and that lies in the first quadrant about the y-axis. Problem courtesy of: http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx Next

11. Determine the volume of the solid obtained by rotating the portion of the region bounded by and that lies in the first quadrant about the y-axis. rewrite the functions: r Volume = Problem courtesy of: http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx Done

12. Next

13. 2 Volume = x f (x) A bit more theory and Next

14. Determine the volume of the solid obtained by rotating the region bounded by and the x-axis about the y-axis. Problem courtesy of: http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx Next

15. 2 Volume = x f (x) Determine the volume of the solid obtained by rotating the region bounded by and the x-axis about the y-axis. Problem courtesy of: http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx Done

16. Questions Back Try the following questions. 1 st Click will bring up a hint. 2 nd click will bring up the answer. 3 rd click will bring up the next question.

17. Determine the volume of the solid obtained by rotating the region bounded by y = x^3 and y = x, about the x -axis.

18. Determine the volume of the solid obtained by rotating the region bounded by x = 2, x = 0, and y = 9 about the y -axis. y

19. Determine the volume of the solid obtained by rotating the region bounded by y = x and, about y = 1.

20. Determine the volume of the solid obtained by rotating the region bounded by y = 2(x^2) - x^3 and the x -axis, about y -axis. Done