Let C Be the Curve X = 2t + Cos $\le$

question 51

Essay

Let C be the curve x = 2t + cos t, y = 4t, z = 2 sin t for 0 $\le$ t $\le$ 3 $\pi$ /2.
Use a potential function to evaluate $\int_{C} \vec{F} \cdot d \vec{r}$ exactly, where $\overrightarrow { \vec { F } } = 4 x ^ { 3 } \cos ( 4 y z ) \vec { i } - 4 x ^ { 4 } z \sin ( 4 y z ) \vec { j } - 4 x ^ { 4 } y \sin ( 4 y z ) \vec { k } \text {. }$

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