Question

4. There is a region O in the plane whose area we wish to compute: JJ, dk dy. It turns out that if we let then in the new coordinates the region Q is described by osu s vand 2 sv s 3. Compute the area of Q.

Answer 1

The Jacobian of the transformation x=g(u, v) and y=h(u, v) is

ax, a(u, v)

Here

LTv

ах ах ду ду 2 7

Hence, Jacobian

6-0 2 2v

dx dy =

r3 cv 6v 10 dudv dx dy =

ax ay = | (6v-10) [11][du

10)

.

dx dy [2(27- 8)-59 4)1 13