- #1
jaredogden
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Homework Statement
I am confused on how exactly Jacobians variables and such. We had a problem on a test in my class that was:
a double integral (i don't know how to use the notation on here) over the region R of (x-2y)e^(x+y)dxdy Where R is the parallelogram with vertices (0,0) (2,1) (2,-2) (4,-1)
We were supposed to chose a change of variables, s and t, based on the integrand and region R. On the key after we got the test back she said s=x-2y and t=x+y
I am confused how exactly she knew that just by looking at the integrand that those were the equations to be used.. I can see graphically how they worked but I am lost as to how it was so easy to tell just from the integrand.
Also what is the correct method to properly convert the region to the new coordinate system based off of that? I can see mathematically how she got the answer for this part on the key online but I don't understand how she got the new graph based off s and t. Any help would be appreciated thanks!
P.S. I hope this was the proper area to post this. It's not exactly a homework question and it's an old test question.
Homework Equations
Jacobian fx,y/fs,t
The Attempt at a Solution
s=x-2y
t=x+y
Jacobian is (1/3)