Transformations

Evaluate the following integral by making an appropriate change of variable.

I don't know how to use the math tags, so I attached it.

I set u = x+y and v=y-2x. Then I note that the sides are x=0, y=0, and x=y. What next?

Like you I don't know Latex so see the attachment

By the way you're region is bounded ny x = 0 , y= 0 and y = 1-x

Its all in the attachment

I got it. Thank you so much for your time! It was very clear and helpful.

In an e-mail I got you said you had difficulty finding x and y in terms of u and v but it seems you figured it out

In case you haven't there are 2 ways

1. Using matrices --see attachment
2.Brute force and ignorance

u =x+y
v = -2x+y

subtract the 2 eqns --this eliminates y solve for x
use the result in either eqn to find y

Yeah, I figured it out. I must have somehow sent the e-mail by mistake. Thanks again for your help.