1. (5 pts.) TRUE OR FALSE: (a) Let R denote a plane region, and (u, v) = (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v) [F(u, v)dudv = [F(u(x, y), v(x, y))dxdy. (b) Let R denote a plane region, and (u, v) = (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then Ldu dudv 1 = √ uzv₁ — u₁vz|drdy. (c) Let R denote a square of sidelength 2 defined by the inequalities || ≤1, y ≤ 1, and (u, v) (3y, 2x). Then the area of R is computed as = LL dudv. (d) Let R denote a square of sidelength 2 defined by the inequalities || ≤ 1, y ≤ 1, and (u, v) (3y, 2x). Then the area of R is computed as = LLave (1/6)dudv. -3 (e) Let R denote a square of sidelength 2 defined by the inequalities |x| ≤ 1, |y| ≤ 1, and (u, v) (3y, 2x). Then the area of R is computed as = LL(1/6)dudu.