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Evaluate line integral

  • Thread starter DryRun
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  • #1
DryRun
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Homework Statement


I have attached the problem to the post.


Homework Equations


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.
 

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Answers and Replies

  • #2
vela
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It looks like you need to either evaluate the integral using the original contour numerically or choose a different path to make the integral doable.
 
  • #3
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... or you could use the Fundamental Theorem for Line Integrals.
 
  • #4
DryRun
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I got the answer key for this today and it involves using the 3rd theorem of line integrals, which converts the line integral into a function, ##\phi (x,y)## and then just evaluate that function over the limits by calculating the two sets of points in terms of x and y. No integration required! At least, not to get the final solution. It's surprising, as the answer is very short.
 

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