(Steps Shown) Evaluate the line integral ∫_C F • d s, where F(x, y, z)=e^z \vecimath+e^x-y \vecjmath+e^y \veck and C is the path consisting of


Question: Evaluate the line integral \(\int_{C} \vec{F} \cdot \mathrm{d} s\), where \(\vec{F}(x, y, z)=e^{z} \vec{\imath}+e^{x-y} \vec{\jmath}+e^{y} \vec{k}\) and \(C\) is the path consisting of straight line segments from \((0,0,0)\) to \((0,0,1)\) and then from \((0,0,1)\) to \((0,1,1)\).

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