Need help on 2 problems involving disk/shell

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Hi again, so I decided to finish my math homework today and get it over with, but had problems with 2 problems on the hw .

Problem #1 (Using Shell method):

x+y^2=9, x=0, revolve about the x-axis  (Find the volume)

The graph of this (I think) would be a parabola on it's side (like a U on it's side would look like a C)  I used the interval [-3,3] because it crosses the y axis or x=0, at -3 and 3. So I integrated (y)(9-y^2) and all that, but end up with 0 as my answer. Any idea what I did wrong?


Problem #2 (Using disk, well it was in the disk section, not sure if you need to use it or not)

"The plane region by y = sqrt(x), y=0, x=0, and x=4 is revolved about the x-axis.  (a) find the value of x in the interval [0,4] that divides the solid into two parts of equal volume.  (b) find the values of x in the interval [0,4] that divide the solid into three parts of equal volume."

I have no idea what to do with this one.  Do you just integrate sqrt(x) and then substitute the x value with 0, 1, 2, 3, and 4?

[Rule]

Hi again, so I decided to finish my math homework today and get it over with, but had problems with 2 problems on the hw .

Problem #1 (Using Shell method):

x+y^2=9, x=0, revolve about the x-axis  (Find the volume)

The graph of this (I think) would be a parabola on it's side (like a U on it's side would look like a C)  I used the interval [-3,3] because it crosses the y axis or x=0, at -3 and 3. So I integrated (y)(9-y^2) and all that, but end up with 0 as my answer. Any idea what I did wrong?


Problem #2 (Using disk, well it was in the disk section, not sure if you need to use it or not)

"The plane region by y = sqrt(x), y=0, x=0, and x=4 is revolved about the x-axis.  (a) find the value of x in the interval [0,4] that divides the solid into two parts of equal volume.  (b) find the values of x in the interval [0,4] that divide the solid into three parts of equal volume."

I have no idea what to do with this one.  Do you just integrate sqrt(x) and then substitute the x value with 0, 1, 2, 3, and 4?

I have long forgotten the terms 'disk' and 'shell' in association with these problems, but both problems seem rather straight forward.

I'm not sure what you mean by "substitute x value with 0, 1, 2, 3, and 4," but if you mean what I think you mean, then absolutely not!

Here's a hint for the second one:  Use sqrt(x) as the radius of your object from x = 0 to x = 4, to obtain the full volume.  Determine what half of the volume is from this.  Then integrate from 0 to x', using sqrt(x) as your radius.  Set this integration equal to half the volume, and solve for x'.  I've basically done part a) of question 2, and part b) follows as an easy extension of this idea.

For problem 1 just pick one of the curves (above or below the x-axis.. your choice), and revolve it around the x axis for x = 0 to x = 9.  In this instance I think you will find it easier to integrate with respect to x.  Ask if you have more questions about this...