- #1
flyingpig
- 2,579
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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]