(adsbygoogle = window.adsbygoogle || []).push({}); Calculating line integrals....

Ok, the problem is:

= 3x (x^2 + y^4)^1/2h(x,y)i+ 6y^3 (x^2 + y^4)^1/2j;

over the arc: y = -(1 - x^2)^1/2 from (-1,0) to (1,0).

In my notes, I had written: ifhis a gradient, then theINTEGRAL of g*dr over curve Cdepends only on the endpoints. Also, if the curve C is closed AND h is a gradient, then theintegral of g*dr over curve cis 0.

So, my question is, when testing to see if a given function like the one above, should you just test to see if:

partial derivative of the?icomponent with respect to y EQUALS the partial derivative of thejcomponent with respect to x

If not equal, then it is not a gradient, right?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculating line integrals

**Physics Forums | Science Articles, Homework Help, Discussion**