Question

its part of a transformation \[u = (1/2)(x+y) , v= (1/2)(x-y) , \to find: \int\limits_{?}^{?} \int\limits_{?}^{?} \sin(1/2)(x+y)\cos(1/2)(x-y) dA\]

how do i Convert to Jacobian over the triangular region R with vertices (0, 0), (2, 0),(1, 1) in terms of U, V