My double integral is (x+y)

where R is the region on the xy plane bounded by the lines

x+y=3, x-y=3, and the hyperbola x^2-y^2=3

(u=x^2 - y^2....v=x+y)

I calculated the jacobian d(u,v)/d(x,y) determinant to be 2(x+y)=2v

and the reciprical = 1/2v

I dont understand what the new integral is and its limits?

my book gives like one example then goes to the next section