# Did my professor make a mistake on the equation of this line integral?

Given F=$(ye^{z} + 2xy, xe^z + x^2, xye^z)$, we want to evaluate the line $\int_c F*dr$. To get the equation, we integrate $f_x$, $f_y$, and $f_z$. Our professor gave us that the equation should be $f(x,y,z) = xye^z + x^2y$, but I'm getting $f(x,y,z) = 2xye^z + x^2y$. This is because I find both $f_x$ and $f_y$ to be $y(x^2+xe^z)$, which when added with $f_z$'s $xye^z$ we see $yx^z+xye^z+xye^z$.

tl;dr: Wouldn't $xye^z+xye^z = 2xye^z$?

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i) your definition of $F$ is incomplete ii) you don't tell us what $c$ is iii) how does $f$ relate to the question? – user20266 Dec 14 '11 at 17:30
It's odd, in my editor for the question I have F=<content>, but when I look at the actual question outside of editor it doesn't show. I'll put it in plaintext – StudentProgramee Dec 14 '11 at 17:40
It didn't like the brackets I had put around the equation. Anyway, you don't need to know $c$, the question is not how to solve the line integral but if $xyez+xyez=2xyez$. I simply put some background so you know where I'm getting this stuff from – StudentProgramee Dec 14 '11 at 17:41

## 1 Answer

1. It seems $\mathrm e^2$ in the definition of $F$ is meant to be $\mathrm e^z$?
2. You don't explain your notation. I gather that $f$ is supposed to be the definite line integral of $F$ from the origin?
3. I don't understand what you write about why you're getting something else, but you can verify that your professor's solution is correct and yours isn't by checking whether the partial derivatives of $f$ equal the components of $F$.
4. Note that your notation for $F$ is rather unusual; vectors are usually enclosed in parentheses.
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