Verify Greens theorem half done

  • Thread starter Jaqsan
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  • #1
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Homework Statement



Verify Greens theorem for the line integral ∫c xydx + x^2 dy where C is the triangle with vertices (0,0) (1,1) (2,0). This means show both sides of the theorem are the same.


Homework Equations


∫c <P,Q> dr = ∫∫dQ/dx -dP/dy dA
∫c xydx + x^2dy

The Attempt at a Solution



Ok, I know the how to verify it with Greens Theorem. My answer comes out to be 1, I just can't figure out the steps to parametrize it or whatever I need to do to solve it without Greens Theorem.

I'm honestly stuck at the first step
∫<P,Q> dr = ∫<xy, x^2> dr
 

Answers and Replies

  • #2
vela
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You have to break the contour up into three pieces. For example, the first leg might go from (0,0) to (1,1). The parameterization you could use would be x=t, y=t, where t runs from 0 to 1.
 
  • #3
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How do I come up with the parameters x=t and y=t. There's no equation to get it from.
 
  • #4
SteamKing
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You examine the piece of the contour under consideration. Remember, t is just a parameter. You are trying to find a relation using t which gives all of the (x,y) coordinates on a straight line segment starting with the point (0,0) and ending at the point (1,1). [Hint: you get to use your imagination. There may be more than one parameterization.]
 
  • #5
vela
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For the given contour, the points (0,0) and (1,1) are connected by a line segment, right? So what would the equation of that line be?
 

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