Drawing the Domain for Double Integral of Function of Two Variable

[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)?

 

[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.

 

[Handala]

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

 

[rootX]

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

http://img508.imageshack.us/img508/2452/graphoy9.png

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

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

 

[HallsofIvy]

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

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?

 

[Handala]

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?

First thanks 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).

 

[Handala]

http://img508.imageshack.us/img508/2452/graphoy9.png

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

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

1st thanks for replying.
I see what you mean, but what if there is no picture of the function. If we only given couple of functions, what the best method to follow to find the region D?

 

[rootX]

1st thanks for replying.
I see what you mean, but what if there is no picture of the function. If we only given couple of functions, what the best method to follow to find the region D?

provide an example.

we can always draw D from functions .. in most simple cases