1. ## Theorem of Green

C is the segment of straight the point $\displaystyle (a,b)$ to point $\displaystyle (c,d)$. Calculate

$\displaystyle \int_C -ydx + xdy$

2. Originally Posted by Apprentice123
C is the segment of straight the point $\displaystyle (a,b)$ to point $\displaystyle (c,d)$. Calculate

$\displaystyle \int_C -ydx + xdy$

Green's Theorem states that

$\displaystyle \int_C{(L\,dx + M\,dy)} = \int{\int_D{\left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right)}}$

Where $\displaystyle C$ is a positively oriented, piecewise smooth, simple closed curve in the plane, and $\displaystyle D$ is the region bounded by $\displaystyle C$.

Here $\displaystyle L = -y, M = x$ so $\displaystyle \frac{\partial L}{\partial y} = -1, \frac{\partial M}{\partial x} = 1$.

But what is your region? All you've given is a straight line. What bounds the region $\displaystyle D$?

3. Originally Posted by Prove It
Green's Theorem states that

$\displaystyle \int_C{(L\,dx + M\,dy)} = \int{\int_D{\left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right)}}$

Where $\displaystyle C$ is a positively oriented, piecewise smooth, simple closed curve in the plane, and $\displaystyle D$ is the region bounded by $\displaystyle C$.

Here $\displaystyle L = -y, M = x$ so $\displaystyle \frac{\partial L}{\partial y} = -1, \frac{\partial M}{\partial x} = 1$.

But what is your region? All you've given is a straight line. What bounds the region $\displaystyle D$?
I thinks all he wants is the line integral along the straight line from $\displaystyle (a,b)$ to $\displaystyle (c,d)$.

4. Originally Posted by danny arrigo
I thinks all he wants is the line integral along the straight line from $\displaystyle (a,b)$ to $\displaystyle (c,d)$.
$\displaystyle ad - bc$