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I've been trying to work out this problem - the answer's $28$, but I can't understand how my textbook gets to that.

I have Vector $\vec F(x,y,z) = yz^2\hat i + xz^2\hat j + 2xyz\hat k$ and $C$ is the path from $(-1,2,-2)$ to $(1,5,2)$ that consists of three line segments parallel to the $z$-axis, the $x$-axis and the $y$-axis.

This implies that I should first integrate the whole thing by parametrizing for $z$ and holding $x$ and $y$ at $0$, then setting $z$ to $2$ and parametrizing for $x$ and then finally parametrizing for $y$ with the values for $x$ and $z$ set.

In all cases this ultimately comes down to an integral of $xz^2$ over some parametrization of $y$ - but how do I select which parametrization? I don't think that this Force field is conservative, so path independence does not occur.

Thanks

2 Answers 2