- #1

- 753

- 2

## Main Question or Discussion Point

u := x (4 - y - x^2)

v := y (-1 + x)

(-2,0)

du := (4 - y - 3 x^2) dx - x dy

dv := y dx + (-1 + x) dy

x := -2 + Cos[\[Theta]]

y := 0 + Sin[\[Theta]]

dx := -Sin[\[Theta]]

dy := Cos[\[Theta]]

Integrate[1/(2 \[Pi]) Expand[(u dv - v du)/(u^2 + v^2)], {\[Theta], 0,

2 \[Pi]}]

If you copy and paste that into mathematica, I'm supposed to get either 1 or -1 but it doesn't work. Does anyone know why?

v := y (-1 + x)

(-2,0)

du := (4 - y - 3 x^2) dx - x dy

dv := y dx + (-1 + x) dy

x := -2 + Cos[\[Theta]]

y := 0 + Sin[\[Theta]]

dx := -Sin[\[Theta]]

dy := Cos[\[Theta]]

Integrate[1/(2 \[Pi]) Expand[(u dv - v du)/(u^2 + v^2)], {\[Theta], 0,

2 \[Pi]}]

If you copy and paste that into mathematica, I'm supposed to get either 1 or -1 but it doesn't work. Does anyone know why?