Question

Calculate the line integral of the vector field vector F = (xy)i + (x-y)j along C, the triangle composed of three segments. C1 is the line segment from (2, 0) to (-2, 0). C2 is the line segment from (-2, 0) to (0, 2). C3 is the line segment from (0, 2) to (2, 0).

Answer 1

Have you considered parameterizing the segments?

Answer 2

It might help you out to draw it, and consider using Green's theorem. Try it both ways to get a feel for which is easier when.

Answer 3

I did the green's theorem and I got it right but the want an answer for C1 C2 and C3

Answer 4

when i do the green's theorem i get -4. but how do I find the answer for each segment?

Answer 5

@tkhunny is the parameter line segment for C1 r(t)=(2-4t)i+0j? I'm not really sure how to do it

Answer 6

how would i do it for each segment @Kainui ?

Answer 7

I'm struggling with you struggling with this. It's a line. You should be familiar with that sort of thing.

1) There is not "the parameter line segment". There are infinitely many ways to parameterize the line segment.

2) You MUST specify the values for 't' for which it is appropriate.

Since there are three segments, some folks like to split up \(t\in[0,1]\)

Using that, \(C1(t) = (-12t + 2)i\;for\; t\in [0,1/3]\)

Answer 8

Yeah