Question

Finding the potential function for a given vector field, original prompt posted below:

Answer 1

http://i.imgur.com/m52GKAP.png

Not sure how to do this, looking up how atm.

Answer 2

\[\int\limits_{}^{}F \cdot dr = f(B)-f(A)\]

Answer 3

@wio (lol I promise I'll stop badgering you soon, test is in two hours)

Answer 4

I'm guessing in order to do this, I have to know that the vector field is conservative, and I can tell that the curl is zero without computing it, so there;s that; Now I'm trying to find the potential function of a conservative vector field.

Answer 5

\[\triangledown f = F\]

Answer 6

I think I need to sort-of integrate some of the components of the given function?

Answer 7

\[x^2+\frac{3}{2}y^2+2z^2=f(x,y,z) \ ?\]

Answer 8

Oh yeah, plus C.

Answer 9

Alright, solved this one right, going to move on to a new type, something about solvinv exact differential forms

Answer 10

Well, you can't always just integrate the components separately.

Answer 11

In this case it works simply due to the fact that you don't have something like: \[
\mathbf F =g(x,y,z)\mathbf i+h(x,y,z)\mathbf j+m(x,y,z)\mathbf k
\]

Answer 12

It's very easy when: \[
\mathbf F = g(x)\mathbf i+h(y)\mathbf j+m(z)\mathbf k
\]

Answer 13

Oh, is this the thing, uh, with, oh god, I really didn't like these.....lol,

Answer 14

The constants that get integrated to become mystery functions of other variables, something like that? I think I know what you're talking about.

Answer 15

Thank you for mentioning that; I'm going to close this one and work on the other one I've said up, which I'm guessing is implicitly asking that I evaluate a line integral in the form of its potential function, and what you said I think will pop up there.