F(x, y, z = yz i xz j (xy 4z k c is the line segment from (3, 0, ? 1 to (6, 4, 1 (a find a function f such that f = ? f. f(x, y, z = (b use part (a to evaluate c ? f · dr along the given curve
c.

Without knowing what the obviously missing symbols could be, I'm going to guess and say that the given vector field is



though I'm not as confident about that last component as I am about the other two.

Now the goal is to find a function such that , which is to say satisfies



Here denotes the partial derivative of with respect to the independent variable .

Integrating the first equation with respect to yields



Differentiating this with respect to gives



Differentiating with respect to , we get



This means you have



and in particular, that , which means the line integral depends only on the value of at the endpoints of its path.

This means