Evaluate the integral along the paths

[Schwarzschild90]

Homework Statement

Homework Equations

and 3. The Attempt at a Solution [/B]

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?

Thank you in advance.

-Schwarzschild

 

[SteamKing]

Homework Statement

View attachment 103046

Homework Equations

and 3. The Attempt at a Solution [/B]
View attachment 103047

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?

Thank you in advance.

-Schwarzschild

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

 

[Schwarzschild90]

Hi SteamKing

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

-Schwarzschild

 

[SteamKing]

Hi SteamKing

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

-Schwarzschild

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

 

[Delta2]

Not sure what you doing there, let's 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?).