Calculating a Line Integral with Greens Theorem

[gtfitzpatrick]

Homework Statement

Calculate \oint _c xdy-ydx where C is the straight line segment from(x_1 , y_1) to (x_2 , y_2)

Homework Equations

The Attempt at a Solution

so from Greens theorem I get \oint _c xdy-ydx = \int\int \frac{\partial x}{\partial x} + \frac{\partial y}{\partial y} dxdy

=2 \int^{x_2}_{x_1}\int^{y_2}_{y_1} dydx
=2[(y_2 - y_1)(x_2 - x_1) ]

 

[LCKurtz]

Homework Statement

Calculate \oint _c xdy-ydx where C is the straight line segment from(x_1 , y_1) to (x_2 , y_2)

Homework Equations

The Attempt at a Solution

so from Greens theorem I get \oint _c xdy-ydx = \int\int \frac{\partial x}{\partial x} + \frac{\partial y}{\partial y} dxdy

=2 \int^{x_2}_{x_1}\int^{y_2}_{y_1} dydx
=2[(y_2 - y_1)(x_2 - x_1) ]

For Green's theorem you need a line integral along a curve which encloses an area. You don't have that so Green's theorem has nothing to do with this problem. Just work the line integral itself out.

 

[gtfitzpatrick]

Hi LCkutz,
Aghhh so he threw it in as a trick question into the greens theorem section. Sneeky!
Thanks LC