Find a function f such that $\mathbf { F } = \nabla f$ and use it to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the given curve C. $\mathbf { F } ( x , y ) = y \mathbf { i } + ( x + 6 y ) \mathbf { j }$ C is the upper semicircle that starts at (1, 2) and ends at (5, 2).

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The Answer of Find a function f such that $\mathbf { F } = \nabla f$ and use it to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the given curve C. $\mathbf { F } ( x , y ) = y \mathbf { i } + ( x + 6 y ) \mathbf { j }$ C is the upper semicircle that starts at (1, 2) and ends at (5, 2).

Find a Function F Such That F=∇f\mathbf { F } = \nabla fF=∇f

Find a Function F Such That $\mathbf { F } = \nabla f$