How do we change the domain?

unded by the st by the st OTtd Example: Evaluate || (y-x)dx dy, over the region Ein the xy-plane bounded hu Solution. It is difficult to evaluate the double integral directly; however a simplo coordinates reduces the domain of integration into a rectangle with sides parallel to the aui lines chang y =X - 3, y = x + 1, 3y + x 5, 3y+ x = 7 s. Set y -x = u, 3y + X = V so that x -3u) y = * u) J16 1J=- 4 and The new domain is the rectangle R = [-3, 1; 5, 7] in uv-plane. -) dx dy udu dv -u du dv --2