00:01
Okay, we want to evaluate this integral.
00:04
We are told that the vector function that's inside here is conservative.
00:11
And it's easy enough to check that.
00:17
So anyway, here's the vector field.
00:24
And we can write, since it's conservative, we can write it as the gradient of some scalar function.
00:35
So we'll start out, phi is integral of the first one times dx.
00:39
And there's an arbitrary function of y and z.
00:51
So we take partial phi with respect to y.
00:54
Comes out to be partial g partial y, is z squared over y.
00:59
So g is z squared log of y, plus a function of z alone.
01:08
We take, here's our phi...