Calculus Question - Please help!

[plzhelp]

Hi everyone,

I'm working on a calculus program and I'm hoping that you all can help. I am trying to find the volume generated by rotating the region about the y-axis enclosed by the graphs y = 9 - x^2 and y = 9 - 3x for x = [0, 2].

Now, I know that you can do this problem by shells, and that the answer turns out to be 8 pi, but I'm wondering if it's possible to do this problem by disks. I've been trying forever and can't seem to figure out the answer by disks. I think it has something to do with splitting it up into separate integrals, but I can't figure it out for the life of me.

Any help would be greatly appreciated!

 

[Rumpltzer]

LOL! Nice first post!

ATOT? Really? That desperate??

 

[Epic Fail]

I don't think any homework will be due this late, you will have the entire evening to do your homework.

 

[plzhelp]

Listen, I already know the answer is 8 pi, and I already know that the answer is done by shells, in other words, v = the integral of (2 pi * (-x^3 + 3x^2)) from x = 0 to x = 2 which is 8 pi. So no, I'm not looking for someone to "do" my homework.

I'm simply curious if this problem can be done by the other volume method I learned, which is by disks. If you know the answer and can share, that would be great, if not, no need to poke fun.

 

[Matthiasa]

It is possible, you just need to find the proper limits of integration.
Really though, just do whats easiest, unless asked otherwise

 

[dighn]

if we help you will you disappear and never to be seen again? anyway the rotation axis is parallel to the axis of the dependent variable (y) so shell is more natural. if you wanna do disk, then you'll need to solve x in terms of y and bound the regions proplery which may not be pretty.

edit: just realized that could be taken the wrong way. I wasn't telling you to go away, but rather think that after getting what you wanted, you'll just leave here.

 

[Hacp]

The formula is pi*radius*radius

 

[DrPizza]

Yes, you can do it using the washer method. However, you're going to have to break it into two integrals.
From y = 3 to y = 5, x = 2 is the outer radius; the line is the inner radius; the parabola doesn't come into play.
From y=5 to y=9, the parabola is the outer radius.

Solving both equations for x yields
sqrt(9-y) for the parabola & (9-y)/3 for the line.

So,
pi * integral (from 3 to 5) of (2²- (9-y)²/9) dy
plus
pi * integral (from 5 to 9) of ( (9-y) - (9-y)²/9) )dy

But the question is, why would you want to do it that way?