Line Integral Around Triangle: Curl or Not?

[mathwizeguy]

Homework Statement

Without parameterizing the path, determine what the value of the line integral (integral of F dot dr) is, if C is the closed, oriented path that travels around the triangle with vertices (0,0) (5,2), and (-3,6) and F=yi + xj

Homework Equations

Curl possiblY?

The Attempt at a Solution

When i attempted this problem i thought i could calculate the line intergral using greens thm but i think it only applies to curves and this is a triangle. does it apply?

 

[Fisicks]

Someone correct me if I am wrong, but Del(xy)=(y,x). Thus the line integral = 10 - 0 + -18-10 +0 +18=0 by the fundamental theorem.

 

[mathwizeguy]

id love to correct you but I am somewhat stumped as to what you mean.\

I am only aware of using the ftc of calculus to caluclate a line intergral with two points but if it works this way then awesome.

 

[Fisicks]

Assuming my method was right, you can just sum the 3 separate line integrals which make up the triangle. After all, a line integral is just the work to go from point a to b, so its like we are summing up joules of energy.