Taking a test (today-Friday) in an hour....anyone available to help please? I just need an explanation to this first part of an example problem. (evaluating integrals by change of variables) Image in comments shows my question.

Question

Taking a test (today-Friday) in an hour....anyone available to help please?  I just need an explanation to this first part of an example problem. (evaluating integrals by change of variables) Image in comments shows my question.

anonymous · Answer

How did they get the y= and x= from that u and v?

ganeshie8 · Answer

solve the system for x and y
$$u = x+y\tag{1}$$
$$v = y-x\tag{2}$$

anonymous · Answer

I know that you are supposed to solve using what you stated above but why don't I see how they got their 1/2(u+v)....
When I do this I get $$v=y-x   \rightarrow y=-x-v $$ and then
$$u=x+y \rightarrow u=x-x-v \rightarrow u=-v  $$

anonymous · Answer

@ganeshie8  thank you for replying...are you able to help clarify my last comment above?

anonymous · Answer

ARGH!!  I got it....I use the Jacobian.  I knew that.... Maybe I need to try sleeping.

ganeshie8 · Answer

u = y+x
v = y-x
------------
u+v = 2y
u-v = 2x

so  (u+v)/2 = y
(u-v)/2 = x

ganeshie8 · Answer

yes you need to find jacobian also for the area scaling factor