Question

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))drdy (b) Let R denote a plane region, and (u,v) (u(x,y),o(x,y)) be a different set of coordinates for the Cartesian plane. Then dudv (c) Let R denote a square of sidelength 2 defined by the inequalities r S1, ly 1, and (u, v)-(3y, 2x). Then the area of R is computed as dudv. 1/2-1/3 (d) Let R denote a square of sidelength 2 defined by the inequalities < 1, lyl <1, and (u, v)-(3y, 2x). Then the area of R is computed as 6dudv. -1/2J-1/3 (e) Let R denote a square of sidelength 2 defined by the inequalities lx-1, lyl 1, and (u, v)- (3y, 2r). Then the area of R is computed as 6dudv.

Answer 1

a), b), and e) are false. When we change the variables, the region doesn't map to R for both coordinate planes.

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