Homework Help: (repost since typos) Volume of revolution using shell method

1. Nov 1, 2009

Call my name

(EDITED)
1. Use the shell method to find the volume of the solid generated by revolving about the y-axis. $$x=y^2, x=y+2$$

2. same as #1, except change y and x for the two equations and revolve about x-axis.

I tried doing $$2pi\int_{x=0}^4(x)(\sqrt{x}-x+2)dx$$ but the answer is off for #1.

I tried doing $$2pi\int_{y=-1}^4(y)(\sqrt{y}-y+2)dy$$, well it's wrong.

Is there a problem with how I established the shell height?

the answer for these two questions are supposed to give me 72pi/5.

2. Nov 1, 2009

tiny-tim

Hi Call my name!

(have a pi: π and a square-root: √ and try using the X2 tag just above the Reply box )
Yeees … it's the shell width, isn't it?
Are you sure that's the question? If you swap everything, isn't the volume the same?

3. Nov 1, 2009

Call my name

Yeah, I meant that those two questions' answers are the same.

So is what I have established wrong?

4. Nov 1, 2009

tiny-tim

You've used height instead of width

(or you've revolved around the wrong axis).

5. Nov 1, 2009

Call my name

What do you mean? I'm a newbie so please specify and clarify