1. ## Linear Transformation

Hey there I need some help with this problem

Let be the region 0 <(or equal to) y <(or equal to) x
0 <(or equal to) x <(or equal to) 1

Evaluate
double integral over D of (x+y) dxdy

by making the change of variables x=u+v, and y=u-v

Check your answers by evaluating the iterated integral directly by using an iterated integral.

Please explain each step you did, so I can understand how to do this problem thanks.

2. ## Re: Linear Transformation

Hey gfbrd.

Its better that you show us your attempt rather than us do it for you. First try using the substitution formula and calculating the Jacobian and post it in this thread.

3. ## Re: Linear Transformation

Yea sorry I have already calculated the Jacobian which is 2, I just dont know how to find the new limits of integration

4. ## Re: Linear Transformation

As a start, x + y = u + v + (u - v) = 2u. Now find the limits in terms of u and v for x = 0 to 1 and y = 0 to x.

Also consider when you make a change of the order of integration (as this may explain why they want to use the new parameterization in terms of u and v).

5. ## Re: Linear Transformation

Alright I figured it out thanks for your help