# How you can say if a line integral will be independant ot a given path

1. May 9, 2014

### gl0ck

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

Here is my problem :

so far I've solved the line integral but I don't know what is the condition that must be met in order to be independant of the path given.
I found the line integral to be: 27/28

Last edited: May 9, 2014
2. May 9, 2014

3. May 9, 2014

### ehild

Try an other path between points (0,0,0) and (1,1,1) . What about a straight line, connecting them?

ehild

4. May 9, 2014

### Feodalherren

If the Curl of the vector field = 0 it is conservative and hence path independent.

How would you find the curl of the vector field?

5. May 9, 2014

### LCKurtz

Open your text and look in the index for "curl"? Or Google it? Or look at the links given in post #2?

6. May 9, 2014

### Feodalherren

I'm not the one looking for help, I was trying to give it :).

7. May 9, 2014

8. May 9, 2014

### HallsofIvy

Staff Emeritus
The integral of a vector function, $\vec{F}$, is independent of the path if and only if it is "a derivative". That is, if there exist a real-valued a function, f, such that $\nabla\cdot f= \vec{F}$. That will be true for this vector function if $f_x= xy$, $f_y= yz$, and $f_z= xz$.

We can check if that is true by looking at the mixed second derivatives: $f_{xy}= x$ and $f_{yx}= z$. Those are NOT the same so this function is NOT independent of the path.