Finding new region for double integral

  • #1
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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?
 

Answers and Replies

  • #2
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Did you draw a sketch?
Did you express u=0 and v=0 in the new coordinates?
 
  • #3
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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?
 
  • #4
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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.
 
  • #5
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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?
 
  • #8
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And if u=v=0 then z=0.
That looks good and it should tell you what to integrate over.
 

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