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When the region enclosed by graphs of y = x and y = 4x - x^2 is revolved about the y-axis, the volume of the solid generated is given by?

The answer is 2*pi*intergral of (3x^2 - x^3) from 0 to 3. Could somebody explain this answer?

Thanks.

By Kevinkleinz (Kevinkleinz) on Sunday, May 02, 2004 - 05:28 pm: Edit

Anyone?

By Cdrotman (Cdrotman) on Sunday, May 02, 2004 - 05:36 pm: Edit

yes, it's volume by shells. 2pi is always there for shells. They intersect at 3. factor out an x and u have your P(x) value, which is the dist from revolution axis. Your H(x) is the height of each shell, which is 4x-x^2-x = 3x-x^2

Eq for shells is: 2pi integral (p(x)*(h(x))dx

By Madd87 (Madd87) on Sunday, May 02, 2004 - 07:51 pm: Edit

Don't worry about it. The Shell method has been dropped from AP

By Altsuperhero (Altsuperhero) on Sunday, May 02, 2004 - 10:35 pm: Edit

they dropped the shell method???

but that was my favorite one ...

and what about vector problems ...

By Billiam2 (Billiam2) on Sunday, May 02, 2004 - 10:46 pm: Edit

Where did you get that from? I have not heard that they dropped the shell method from the test.

By Justice (Justice) on Sunday, May 02, 2004 - 11:40 pm: Edit

Haha dropping shells...

no.

By Mk1o3o (Mk1o3o) on Monday, May 03, 2004 - 05:20 am: Edit

calculus is so fun...

By Athlonmj (Athlonmj) on Monday, May 03, 2004 - 07:26 am: Edit

I'm pretty sure shell is dropped as well. At least that is what my teacher told us. She still taught it to us for fun.

By Madd87 (Madd87) on Monday, May 03, 2004 - 05:28 pm: Edit

Shell was dropped a while ago. This is not news.

By Qwert271 (Qwert271) on Monday, May 03, 2004 - 09:51 pm: Edit

Wow. I'm in AB and I know how to do that. Next year's gonna be fun.

By Kevinkleinz (Kevinkleinz) on Monday, May 03, 2004 - 10:10 pm: Edit

Sorry. My teacher just didn't go over the shell method. Oh well. Thanks everybody.