# Question: let 0 lt a lt b two given reals let...

###### Question details

Let
0 < a < b two given reals. Let D be a strip-like domain in
R^2 bounded by the curves x = 0, y = 0, y = a - x, and y = b - x.
Let us define moreover G: R^2 —> R^2 as G(u,v) = (u - uv, uv).

1. Show that the image of the horizontal line v = c is y =
((c) / (1-c))(x) if c does not equal 1 and it is the y-axis if c =
1.

2. Determine the images of vertical lines in the uv
plane

3. Compute the Jacobean determinant of G at any arbitrary
point (u, v).

4. Compute the area of D using two methods: first see your
domain as a vertically or horizontally simple one (you may
decompose it into two pieces) and compute the volume as an iterated
double integral. Then use the change of variable formula applied to
G and compute the area once again.

5. Compute the double integral of xy dA on D using the
previous two methods again.