1. ## Theorem of Green

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

$\int_C -ydx + xdy$

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

$\int_C -ydx + xdy$

Green's Theorem states that

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

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

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

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

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

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

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

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

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

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