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## Homework Statement

Given [tex]\mathbf{F} = \nabla f\; where \;f(x,y) = sin(x-2y)[/tex]

Find a curve C that is not closed and satisfy the equation

[tex]\int_C \mathbf{F}\cdot dr = 0[/tex]

## The Attempt at a Solution

[tex]\nabla f = \;<cos(x - 2y),-2cos(x-2y)>[/tex]

So to satisfy the dot product being 0 (I am hoping I can do this)

cos(x - 2y)dx = -2cos(x-2y)dy

dx = -2dy

[tex]y = \frac{-t}{2}+K[/tex]

[tex]x = t[/tex]

[tex]t \in [a,b][/tex]

I am just wondering, am I doing this correctly...?

**Solutions**

My book just took [tex]r(t) = t<\pi,\pi>[/tex]