Calculating the Shell Method for 2π∫x(9x⁴/625)dx

[xdrgnh]

Homework Statement

http://www.catholiccentral.net/Document.Doc?id=200 problem number 5

Homework Equations

2pi intergral x(9x^4/625)

The Attempt at a Solution

When I do the shell method it doesn't give me the same answer as if I use disk. I've also noticed that when I do the shell method on the function x^4 it gives a different answer then when I use the disk method. I know what the answer is. My main question is why is there a 9-9x^4/625 in for the height in the solution instead of just a 9x^4/625.

 

[Dick]

Your method would be correct if you wanted the volume underneath the rotated curve. But you don't want that. You want the volume contained between y=9 and the rotated curve y=9x^4/625. So the width of the shell is the difference of those two values.

 

[xdrgnh]

Your method would be correct if you wanted the volume underneath the rotated curve. But you don't want that. You want the volume contained between y=9 and the rotated curve y=9x^4/625. So the width of the shell is the difference of those two values.

Oh I think I get it, so the radius would just be x and the height would be the top height 9 minus the bottom height y which is given by y=9x^4/625

 

[Dick]

Oh I think I get it, so the radius would just be x and the height would be the top height 9 minus the bottom height y which is given by y=9x^4/625

Exactly.

 

[xdrgnh]

Exactly.

Thanks a lot, have a happy new year