Compute the Jacobian of the Transformation T Given By $x = v \cos 2 \pi u$

Essay

Compute the Jacobian of the transformation T given by $x = v \cos 2 \pi u$ , $y = v \sin 2 \pi u$ . Describe the image of $S = \{ ( u , v ) \mid 0 \leq u \leq 1,0 \leq v \leq 1 \}$ , and compute its area.