Exercise 3. Consider the integral I-2y dA 24 3x-y where R is in the (x, y)-plane bounded by the lines x-2y= 0, x-2y= 4, 3r-y=1, and 3r-y=8. (25 points) (a) Find a change of variables u and v such that the region R becomes a rectangle in the (u, v)-plane. R = { 0 x-2y 4, 1 3 x - y < 8} S Let M=x-24 V= 3x-y (2.5) (2.5) (b) Express the double integral above in terms of (u, v). x = 2v - M+1. Find x 5 J(40) = y = V zu Find y 8 Flu,v) = S u V Find Flu, v). +1 10 pts 6 + 25 25 525 +1 determinant +4 Jacobian dudr +2 (bounds are correct +1 Structure of integral is correct +1) e.g. if (J(UN)), F(u,v), etc..