Answer:
Step-by-step explanation:
Given that R is a treapezium with given vertices in the xy plane with side 3 units.
Substitution is
[tex]x=u-uv\\y=uv[/tex]
[tex]J =\left[\begin{array}{ccc}x_u&x_v\\y_u&y_v\\\end{array}\right] \\=1-v v\\ -u u\\=u-uv+uv =u\\[/tex]
Hence dx dy = ududv
Integrand = [tex]\frac{1}{x+y} =\frac{1}{u}[/tex]
Limits now we have to change
We see from the vertices the line x+y changes from 1 to 4, i.e. 1<u<4 and
we get [tex]v=\frac{y}{u} =\frac{y}{x+y}[/tex] so v varies from 0 to 1
The given integral
=[tex]\int\limits^4_1\int\limits^1_0 {\frac{1}{u} } \u du\\ =(4)(1)\\=4[/tex]
