Note that all your limits involve x+y or x-y, and that part of your integrand is (x+y). Does this suggest a choice for u and v?
--Kevin C.
Hi Guys,
I'm having troubles starting this problem. In the previous problems we have had, our transformation has been given to us (i.e something like x=u+v,y=u-v etc...). Since one is not given here do I just use x as u and y as v? Any help with this nasty would be greatly appreciated.
Evaluate the integral where R is the rectangle enclosed by the lines
x - y = 0,
x - y = 2,
x + y = 0,
x + y = 3.
Use a change of variable and a Jacobian.
Where
So letting and , we see that we have the limits and
Now we need to find equations for x and y in terms of u and v.
since , we see that
Therefore,
Now let's find an equation for x.
since , we see that
Therefore,
Now, let's find the Jacobian .
Now change the variables of the integral:
Can you try to integrate this? I think you can take it from here.
--Chris