1. Math
  2. Advanced Math
  3. let 0 lt a lt b two given reals let...

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.

Let 0 < a b two given reals. Let D be the strip-like domain in R2 bounded by the curves 0, y 0, y- a- x and y b-x. Let us define moreover G: R R2 as G(u,v) (u-uo,uw). (1) Show that the image of the horizontal line u c is y-tex if c#1 and it is the y-axis if c-1. (2) Determine the images of vertical lines in the uOv plane. (3) Compute the Jacobian determinant of G at an arbitrary point (u, v). 1-c
(4) Compute the area of D using two methods: first see your domain as a vertically or horizontally simple one (you may also 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 once again the area. (5) ComputeydA using the previous two methods again. J JD
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution