# Finding new region for double integral

• I
• Mr Davis 97

#### Mr Davis 97

I have a double integral where the region of integration is ##R = \{(u,v) : 0 \le u < \infty, ~0 \le v < \infty) \}##. I am doing the change of variables ##u=zt## and ##v = z(1-t)##. I am a bit rusty on calc III material, so how would I find the new region of integration, in terms of the zt-coordinate system?

Did you draw a sketch?
Did you express u=0 and v=0 in the new coordinates?

Did you draw a sketch?
Did you express u=0 and v=0 in the new coordinates?
Will I know that in uv coordinates the region is the first quadrant.

If u=0, then z=v.
If v=0, then z=u.

Does this help me in any way?

If u=0, then z=v.
If v=0, then z=u.
These are not the only options, and you are trying to do two steps at the same time. Do it step by step.

These are not the only options, and you are trying to do two steps at the same time. Do it step by step.
If ##x=0,y \ne 0##, then ##z=y,t=0##
If ##y=0,x \ne 0##, then ##z=x, t=1##.

Is this correct?

What are x and y?

What are x and y?
Sorry, replace x with u and y with v.

And if u=v=0 then z=0.
That looks good and it should tell you what to integrate over.