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Question

In given problem, show that the given line integral is independent of path (use Theorem C\mathrm{C} ) and then evaluate the integral (either by choosing a convenient path or, if you prefer, by finding a potential function f and applying Theorem A).

(0,1,0)(1,1,1)(yz+1)dx+(xz+1)dy+(xy+1)dz\int_{(0,1,0)}^{(1,1,1)}(y z+1) d x+(x z+1) d y+(x y+1) d z

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Answered 2 years ago
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F=yz+1,xz+1,xy+1\begin{align*} \mathbf{F} &= \left\langle yz+1,xz+1,xy+1\right\rangle \end{align*}

Determine the vector F\mathbf{F} from the integrand.

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