Question: Let \(\mathbf{F}=\left( \frac{1}{y}+2z \right)\mathbf{i}+\left( z-\frac{x}{{{y}^{2}}} \right)\mathbf{j}+\left( y+2x \right)\mathbf{k}\) and let \(f\left( x,y,z \right)=x+y+z\) .

1. Let C1 be the segment from (1, 1, 1) to (2, 2, 2). Compute both \(\int\limits_{{{C}_{1}}}{fds}\) and \(\int\limits_{{{C}_{1}}}{\mathbf{F}\cdot dr}\)
2. Let C2 be the curve parametrized by \(r\left( t \right)=t\mathbf{i}+{{e}^{{{t}^{3}}}}\mathbf{j}+{{t}^{2}}\mathbf{k}\) for \(0\le t\le 1\) . Compute \(\int\limits_{{{C}_{2}}}{\mathbf{F}\cdot dr}\) explaining your work.

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