Evaluate the following integral using change of variables. Draw the original and new regions of integration.
$$\int\int_{R} \frac{1}{x^2-y^2} dA$$
where R is bounded by the lines
$x + y = 1 ,x + y = e, x − y = 1, x − y = e$
I am used to seeing problems where the desired transformation is given, but I don't understand how to make my own region. Are the new regions simply the partial derivatives of the region given?
"partial derivatives of the region given" doesn't make sense.
But what does make sense is to use the form of $x$ and $y$ given for the region. That is, try $u = x + y$ and $v =x - y$. Then the region in the new coordinates is just $1 \rightarrow e$ for both.
Note also that $uv = x^2 - y^2$. Can you take it from there?