- #1

- 43

- 0

## Homework Statement

Use greens theorem to solve the closed curve line integral:

[itex]\oint[/itex](ydx-xdy)

The curve is a circle with its center at origin with a radius of 1.

## Homework Equations

x^2 + y^2 = 1

## The Attempt at a Solution

Greens theorem states that:

Given F=[P,Q]=[y, -x]=yi-xj

[itex]\oint[/itex]F*dr=[itex]\oint[/itex]Pdx+Qdy=[itex]\int[/itex][itex]\int[/itex]([itex]\frac{dQ}{dx}[/itex]-[itex]\frac{dP}{dy}[/itex])dA

From the circle equation i find:

x=[itex]\sqrt{1-y^2}[/itex]

y=[itex]\sqrt{1-x^2}[/itex]

Which means that:

[itex]\frac{dQ}{dx}[/itex]=0 and [itex]\frac{dP}{dy}[/itex]=0

Obviously, I am doing something wrong... but which rules am I breaking??

I did find the answer the "normal" way, without greens, which was -2[itex]\pi[/itex].

I think a lot of my difficulties originates from lack of knowledge about different coordinate systems and the conversion between these.

One could write:

x=cos t and y=sin t, but do I have to? (btw, i used that for solving the normal way).