$1$

The vector field $G(x,y,z)=z{e}^{x}i+1j+e^{x}k$ is conservative.

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True

False $$

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$2$

Mar

Calculate the line integral of $G(x,y,z)=z{e}^{x}i+1j+e^{x}k$ along the curve $C$ parametrised by $r(t)=tcos(2t)i+tj+sin(2t)k$ for tin$[0,1]$ :

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}G*dr=$

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