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# \begin{array}{c}{\text { Use the transformation in Exercise } 2 \text { to evaluate the integral }} \\ {\int_{0}^{2 / 3} \int_{y}^{2-2 y}(x+2 y) e^{(y-x)} d x d y} \\ {\text { by first writing it as an integral over a region } G \text { in the } u v \text { -plane. }}\end{array}

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{'transcript': "Hi, guys. For 27 who wants me and simplify the expression two ex wives in the native to over three x squared y two. Oops. Forgot the negative one. So now what we're gonna do is I'm gonna do the top part first. I didn't do anything to the two eggs, but with the whites of the negative too. I will actually take that down to the bottom one. Now have to fax over three x squared y the native one y squared came. Now we can go to simplify the bottom by distributing the negative one son and about three native one x squared times negative. Why it's in the negative one all of that Times Square Now in doing so, the three to the negative one I will leave. Is that because with the negative one out and I'll take that whole number up to the top and up with X's and the negative to and why to the negative times, Why squared now? Since I have this down here, all you have to do is combine my life terms in combining my like terms. I now end up with point of the negative one or positive when I'm sorry. Why? To the positive one. And that now stays on the bottom. This have here of three dominated one. An excellent native to needs to move to the numerator. So I now have two times three, which will give me a six have x squared and eggs which gives me X cubed in my numerator. All of that over. Why? So that will be my"}

The University of Texas at El Paso

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