Line integral

  • #1

Homework Statement



F=<xy, x-y> and C is the triangle joining (1,0), (0,1) and (-1,0) in the clockwise direction.

Homework Equations



How do I have the second part of this curve?

The Attempt at a Solution


Apparently, there should only be a sum of two integrals. So I got that curve one could be
[tex]C_1: x=t, y=0, -1≤ t ≤ 1[/tex]

But I have no idea how to find [tex]C_2[/tex]. There's no other way, that I see, that you can take such that you keep x constant and let y vary.
 

Answers and Replies

  • #2
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0
The reason it should only be a sum of two integrals is because the line integral is just zero on the curve you have. You're only interested in the sum of the integral over [itex]C_2[/itex] and [itex]C_3[/itex]. How might you parametrize those? For example, if you wanted to find a line in x-y coordinates to go from (1,0) to (0,1), you would find its slope (-1) and its y-intercept (1). The line would be y = 1-x. So if you let x = t, then what would y be and what would t vary between?
 

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