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