I have attached the problem to the post.
Properties of line integral. Path independence.
The Attempt at a Solution
I have shown that the path is independent, as:
[tex]\partial P/\partial y = \partial Q/\partial x[/tex]
The problem is with the parametrization. I found ##dx/dt## and ##dy/dt## and replaced into the line integral as well as x and y, so i have the line integral in terms of ##t## only. But the expansion becomes such a mess. I don't know if there's some simplification to be done, before integrating w.r.t.t. If not, then i'm stuck. I have a doubt that the path being independent has something to do with the simplification of the evaluation of line integral, but i can't figure how.
18.1 KB Views: 405