Prove if a vector field is conservative or not

[jessedevin]

How do you prove if a vector field is conservative or if it isn't conservative?
For example, if we have the vector field F(x, y, z) = x^2yz ı + y  + x^2 k, how do we find out if it is conservative or not conservative?

 

[ZapperZ]

Find the curl of that vector field, and figure out the significance if it is zero.

Zz.