6.3 Volumes by Cylindrical Shells

1-18. Find the volume generated by rotating the region bounded by the given curves about the -axis using the method of cylindrical shells.

1. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-1.html

 4*pi


2. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-2.html

 


3. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-3.html

 


4. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-4.html

 

   


5. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-5.html

 

      

   


6. about .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-6.html

     


7. about .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-7.html

    

  


8. about the axis.

http://matrix.skku.ac.kr/cal-lab/cal-6-3-8.html

      


9. about .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-9.html

   

   


10. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-10.html

.


11. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-11.html

.


12. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-12.html

.


13. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-13.html

.


14. .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-14.html


15. about the axis.

http://matrix.skku.ac.kr/cal-lab/cal-6-3-15.html

  

    


16. about .

http://matrix.skku.ac.kr/cal-lab/cal-6-3-16.html

   

   


17. about the axis.

http://matrix.skku.ac.kr/cal-lab/cal-6-3-17.html

 

  


18. about the axis.

http://matrix.skku.ac.kr/cal-lab/cal-6-3-18.html