# Change of variables-multiple integrals

• February 16th 2009, 12:46 PM
Andreamet
Change of variables-multiple integrals
Let R be the re gion enclosed by
x-y = 0
x- y = 2
x + y = 0,
x + y = 3.
USING CHANGE OF VARIABLES, evaluate

$\int \int_R(x+y)e^(x^2-y^2) da$
• February 16th 2009, 12:52 PM
Krizalid
$R=\left\{ (x,y)\in \mathbb{R}^{2}|0\le x-y\le 2,\,0\le x+y\le 3 \right\}.$

Make the substitution $(u,v)=(x-y,x+y)$ so that $0\le u\le 2$ and $0\le v\le3.$ Don't forget the Jacobian.