# Cartesian coordinates problem

1. Jul 8, 2009

### jeff1evesque

1. The problem statement, all variables and given/known data
Solid horn obtained by rotating the points $${[x=0], [0 \leq y \leq 4], [0 \leqz \leq \frac{1}{8}y^{2}] }$$ circles around y-axis of radius $$\frac{1}{8}y^2$$. Set up the integral dzdxdy.

2. Relevant equations
Cartesian coordinates.

3. The attempt at a solution
I don't understand how the z-limits are $$\pm \sqrt{\frac{y^4}{64} - x^2}$$? I understand that the z limits must involve x and y, but cannot come up with the latter conclusion.

Thanks

Last edited: Jul 8, 2009
2. Jul 8, 2009

### Ja4Coltrane

Re: Integrating

I think you have some typos. It's not clear what you mean here. You have, for instance, 0 is less than or equal to y^2/8. That gives no information as y^2 is greater than or equal to zero for all real numbers y.

3. Jul 8, 2009

### jeff1evesque

Re: Integrating

Well I suppose without looking at a picture, that may be a reasonable opinion- and hard to interpret. I've attached a picture, if that helps any.

Thanks a lot

JL

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Last edited: Jul 8, 2009
4. Jul 8, 2009

### jeff1evesque

Re: Integrating

I guess I am having difficulty determining the limits of this particular integration (in cartesian) along the z-axis.

5. Jul 8, 2009

### Staff: Mentor

Re: Integrating

It sometimes takes several hours for an attachment file to be approved, so if you could describe the solid in words, that would be helpful.

My guess as to how you have described the solid so far is that the curve in the x-y plane, x = y2/8, is revolved around the y-axis to form a solid. And you want the portion of this solid between the planes y = 0 and y = 4.

Is this a reasonable description?

6. Jul 8, 2009

### jeff1evesque

Re: Integrating

Yup that sounds reasonable. Basically, if you could picture then end of a horn [perhaps a trumpet, beginning as a point on the origin and expanding out along the y-axis] with the y-axis going through the center, that's what this image looks like. At y = 4, the "horn" has a height of z = 2, which obviously rotates around the y-axis.

7. Jul 9, 2009

### jeff1evesque

Re: Integrating

I actually solved this problem this morning with some help from other.

Thanks,

JL