Math Help (Triple Integrals)
 

I'm just going over some of my problem set that's due tomorrow and for some reason I've ran into this problem on Triple Integrals and can't seem to get an answer that makes sense. Just wondering if someone here could enlighten me:
Any help is greatly appreciated.

Find the volume of the body above the xy plane, below the cone z = (x² + y²)½, and inside the sphere x² + y² + z² = 3.

My main problem is figuring out the bounds on the integrands. Thanks in advance.

I don't know, but your post makes me not miss my college days.

I have actually forgotten how to do this.

I'm now trying to figure out one of my great quandries in Mathematics though, thank you. Grrr. Not to thread jack but it was a problem with the discrepancy when solving the area beneath and the volume of the cone generated by rotating the function y=1/x around the X axis. Somesuch guys Trumpet.. IIRC the area is infinite, but when swept around the axis it yields a finite volume..or the exact opposite. I have never been able to resolve it either way, and it was the point in my mathematics schooling where I quit trying to really understand things, and just did what I was told. Anyway once I remember how to do that I'll throw some brain cells at your question.

You have to break the region up into 2 parts.

1: The cone below the plane where the sphere intersects it.
2: The part above where the sphere intersects.

The bottom part should be easy enough to find bounds on. It's just a solid cone.
The top part is a little bit harder, but not too bad. It's just a small slice of a sphere.

is our children learning?

If all you need is an answer, I'd recommend Monte Carlo integration. :p

I prefer seperate but equal.

I may have a degree in Math, but I can't even tell you where to begin. I only got said degree because I passed Calc III by the skin of my teeth. I hates Calculus.

After you figure this out, ran yourself into an English class. ;)

(I forget how to do this too...my college loans have outlasted my memory)

English never was my favorite subject...though math is proving to be a pain these days also.

Heck, I'm taking an advanced Chemical Engineering math class and I couldn't tell you (aside from using Monte Carlo integration, which is just a cool technique). I can solve second order differential equations using Bessel functions, but not this... :p

(Of course, this part of Calc 4 was the part that I never really got the hang of doing...)

I have a relative who goes to Boston University.

I can't remember how to even solve the silly equation I was trying to recall. So I am eons from figuring it out. I'll ask my wife, she is actually the math major. She's busy with a screaming kid right now, but she may feel like digging in once the little one is down for the evening.