Let i=∫∫d(x2−y2)dxdy, where

d={(x, y): 3≤xy≤6,0≤x−y≤7,x≥0,y≥0}

show that the mapping u=xy, v=x−y maps d to the rectangle r=[3,6]×[0,7].

(a) compute ∂(x, y)/∂(u, v) by first computing ∂(u, v)/∂(x, y).

(b) use the change of variables formula to show that i is equal to the integral of f(u, v)=v over r and evaluate.

(a)∂(x, y)/∂(u, v)=

(b)i=