In this problem we use the change of variables x=5s+tx=5s+t, y=s−ty=s−t to compute the integral ∫r(x+y)da∫r(x+y)da, where rr is the parallelogram with vertices (x, y)=(0,0)(x, y)=(0,0), (5,1)(5,1), (6,0)(6,0), and (1,−1)(1,−1).

The Jacobian matrix for this transformation is

The vertices in the plane correspond to the following points in the plane:

That is, the parallelogram is mapped to a square in the plane, so

hiking down a winding trail.

step-by-step explanation: