Let P be the parallelogram with vertices 005162 and 11 Let f

Let P be the parallelogram with vertices (0,0),(5,1),(6,2) and (1,1). Let f(x,y)=7x+y . Find a linear change of variable (x,y)=T(r,s)=(ar+bs,cr+ds) so that (1,1)=T(0,1) and (5,1)=T(1,0) so that Pf(x,y) dx dy over P becomes Sf(T(r,s))|Jacobian(T)| dr ds over the square S 0r , r1 , 0s , s1 . Then evaluate this second integral.

Solution