- #1
oferon123
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Homework Statement
Find surface inside four boundary curves:
[itex]xy = 4 , xy=8 , y=5x , y=15x[/itex]
using the transformation: [itex]u=xy , v=\frac{y}{x}[/itex]
Homework Equations
I'm getting the new bounds to be:
[itex]4 < u < 8[/itex] , [itex] -15 < v < -5 [/itex] OR [itex] 5 < v < 15[/itex]
Jacobian is [itex]\frac{1}{2v}[/itex]
The Attempt at a Solution
After integration i get [itex]0.5*ln(v)[/itex] which I can't put -15 nor -5 in it..
On the solution they gave us, they completely ignore the surface at x,y < 0 and go only for 5 < v < 15 , which I assume is only relevant for the surface at x,y > 0...
As if they calculated only the half of the area.
I understand all I need to do is double this area, but where am I going wrong?
I attach this sketch I've drawn trying to understand what's going on:
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