# How to draw the domain of a function of two variables to find the double integral

1. Jul 18, 2008

### Handala

This is not for a specific problem, just in general:
If we want to find the double integral of a function of two varaible, when we got other 1 varaible function to define the domain. What are the basics of drawing the domain in 2d (x, y only)?

2. Jul 18, 2008

### Defennder

What does "other 1 variable function" refer to? I don't see what the domain of the function f(x,y) has got to do with the double integral of f(x,y) over a given region.

3. Jul 18, 2008

### Handala

All I meant is how to fine the region D of the function to know the limits of each variable?

4. Jul 18, 2008

### rootX

http://img508.imageshack.us/img508/2452/graphoy9.png [Broken]

rule is first define limits for the changing var (see blue line), and then integrate constants.

Limit is simply f(x) to g(x)

Last edited by a moderator: May 3, 2017
5. Jul 19, 2008

### HallsofIvy

Staff Emeritus
How you do that depends strongly on the particular region. Since you say this is for a specific problem, what is the specific problem? What region are you talking about?

6. Jul 19, 2008

### Handala

First thx for replying. I said its not for a specific problem. However, let's take this for any example:
(Find the volume of the solid that lies under the paraboloid z=x^2+y^2, above the xy-plane, and inside the cylinder x^2+y^2=2x.)
I think we should convert to Polar coordinate. I know how to find r, but the problem is how to find the angle (theta).

Now for other problems, when you have the couple of function, how do we find the the region D, I know some would say draw the function, but some functions are hard for me to draw them. Hope some one knows a techinque of how to find the limit or the region D (The domain).

7. Jul 19, 2008