Question 2016.S2.31: The line integral of the vector field F = 5xzi^? + (3x²+2y)j......

Wiley Acing The Gate Electrical Engineering [1079382]

The line integral of the vector field $F=5 x z i^?+\left(3 x^2+2 y\right) j^?+x^2 z k^{?}$ along a path from (0, 0, 0) to (1, 1, 1) parametrised by (t, t², t) is ________.

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Given that

$\begin{aligned}& E=5 x z i^?+\left(3 x^2+2 y\right) j^?+x^2 z k^? \\& =\int_C \vec{F} \cdot d \vec{r} \\& =\int_0^1 5 t^2 d t+\left(3 t^2+2 t^2\right) 2 t d t+t^3 d t=4.41\end{aligned}$

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