Thread: Integration via shell method

Reviewing for my final and got one (of many) problems I keep getting a weird answer for. The problem reads:

Use the shell method to integrate. Find the volume generated by revolving the region bounded by the graphs of and about the line .

Using the shell method I set it up as from [1,2]. However, I get a negative volume. Any help would be greatly appreciated.

Thanks

Originally Posted by Poptimus

Reviewing for my final and got one (of many) problems I keep getting a weird answer for. The problem reads:

Use the shell method to integrate. Find the volume generated by revolving the region bounded by the graphs of and about the line .

Using the shell method I set it up as from [1,2]. However, I get a negative volume. Any help would be greatly appreciated.

Thanks

Well, you have forgotten to put parentheses around (x-1), that's why you get a negative result. Also, you have left out a factor of , I believe.

Well, one possible reason you're getting negative numbers is that you should have



Sign error in there will do it every time. I think you also forgot the factor out front. Don't forget: with the shell method, you could slice up one shell, flatten it out, and you'd have a rectangular prism whose volume is quite easy to compute: The radius , like you had.

[EDIT]: Failure failed to allow my post to go first.

Appreciate it guys, such a simple mistake. I can't believe I overlooked it.