# Evaluate the integral along the paths

1. Jul 10, 2016

### Schwarzschild90

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

2. Relevant equations and 3. The attempt at a solution

The assignment that I'm struggling with can be seen under the heading titled 1. and my attempt at a solution can be seen in 2. and 3.

Obviously, what I'm doing is wrong. I've surely misunderstood the problem statement. Will someone please help me?

-Schwarzschild

2. Jul 10, 2016

### SteamKing

Staff Emeritus
There seems to be only two attachments to your post. I think attachment #3 is missing.

3. Jul 10, 2016

### Schwarzschild90

Hi SteamKing

There's no third attachment, sorry, English is not my first language.

-Schwarzschild

4. Jul 10, 2016

### SteamKing

Staff Emeritus
You seem to be ready to evaluate z between the applicable limits, but you don't appear to show a final result.

5. Jul 10, 2016

### Delta²

Not sure what you doing there, lets take

(I) for the path $(x_1,y_1)->(x_2,y_1)->(x_2,y_2)$ (going through straight line segments) we ll have

$\int\limits_{(x_1,y_1)}^{(x_2,y_2)}2xydx=\int\limits_{(x_1,y_1)}^{(x_2,y_1)}2xydx+\int\limits_{(x_2,y_1)}^{(x_2,y_2)}2xydx=\int\limits_{(x_1,y_1)}^{(x_2,y_1)}2xydx+ 0=(x_2^2-x_1^2)y_1$.

You can work similar for $\int (x^2+2xy)dy$ seeing that it ll be zero for the straight line segment$(x_1,y_1)->(x_2,y_1)$ so you need to evaluate it only for the straight line segment $(x_2,y_1)->(x_2,y_2)$

Then you should calculate same things for the path in (II)

If the answer you get in (I) is different than that in (ii) then we can safely say that it is not an exact differential (why?).