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

Short Answer

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).