Let (u, v) = (u uv, uv). (a) Show that the image of the horizontal line

Let Φ(u, v) = (u − uv, uv).
(a) Show that the image of the horizontal line v = c is y = c / 1 − c x if c ≠ 1, and is the y-axis if c = 1.
(b) Determine the images of vertical lines in the uv-plane.
(c) Compute the Jacobian of Φ.
(d) Observe that by the formula for the area of a triangle, the region D in Figure 14 has area 1/2 (b² − a²). Compute this area again, using the Change of Variables Formula applied to Φ.
(e) Calculate

Transcribed Image Text:

SS D xy dx dy.