Finding Volume Using Triple Integrals: A Brief Guide

[synergix]

Homework Statement

i have to find the volume between the function z=4-x^2-y^2 and the x/y plane

The Attempt at a Solution

I think I should be fine with the limits of integration but am not 100% confident what I am integrating.

is it 4-x^2-y^2-z??

or 4-x^2-y^2?

 

[synergix]

So I'm just going to integrate dv I think this might be correct. my bounds would be x=0->sqrt(y^2-4) then y=0->sqrt(z-4) then z=0->4. And then I would integrate in this order. Is this correct?

 

[jackmell]

Why not convert to polar coordinates? Then z=4-r^2 right? I assume you mean positive z, the paraboloid above the x-y plane. It's symmetrical so you could just integrate in the first quadrant and multiply by four:

$$V=4\int_0^{\theta_0}\int_0^{r_m} (4-r^2)rdrd\theta$$

Can you understand how I did that and come up with the values for $\theta_0$ and $r_m$?