Question

Compute midpoint approximation of
∫R f(x,y)dA for n=4 where f(x,y)=2^(x^2-2xy+y^2) and the Region R= [-2,2] x [0,2]

Answer 1

Why a numerical approximation when you can evaluate it directly. Setup a diffeomorphism first from a rectangle to a disk to an ellipse then apply the change of variables theorem. You can probably evaluate it directly.