how to i check if these forces are conservative?

Question

anonymous · Answer

F = [x^3 + y, y^3 + x, 2]

and 

F = [yz, xz, xy]

jamesj · Answer

Forces are conservative if they are curl free, because by Stoke's Theorem, if the curl of the vector field is zero, then the line integral along any path of F is also zero. The latter is the definition of conservative.

So take the curl of these two vector fields and see if they are identically zero or not. If yes, they are conservative; if not, they are not.

anonymous · Answer

well i the thing is i checked up the curl of forces in wikipedia. i don't understand a thing how to calculate this :(. i have a test tomorrow and I KNOW this question will pop up. can you please help me calculate this? @JamesJ

jamesj · Answer

This takes a good 20 minutes or so to explain well. Watch this video and the one that follows: https://www.khanacademy.org/math/calculus/partial_derivatives_topic/curl/v/curl-1

anonymous · Answer

thanks a lot!

jamesj · Answer

What did you find? Is the first and second F conservative or not?