# Verify Greens theorem half done

1. Aug 12, 2013

### Jaqsan

1. The problem statement, all variables and given/known data

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.

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

3. 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

2. Aug 12, 2013

### vela

Staff Emeritus
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. Aug 12, 2013

### Jaqsan

How do I come up with the parameters x=t and y=t. There's no equation to get it from.

4. Aug 12, 2013

### SteamKing

Staff Emeritus
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. Aug 12, 2013

### vela

Staff Emeritus
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?