Let $\vec{F}$ Be a Conservative Vector Field with Potential Function G Satisfying

Short Answer

Let $\vec{F}$ be a conservative vector field with potential function g satisfying g(0, 0)= -5.Let C₁ be the line from (0, 0)to (2, 1), C₂ the path parameterized by $\vec { r } ( t ) = ( 2 + 2 \sin t ) \vec { i } + \cos t \vec { j } , \quad 0 \leq t \leq \pi$ and C₃ the path parameterized by $\vec { r } ( t ) = ( t + 2 ) \vec { i } + \left( t ^ { 2 } - t + 1 \right) \vec { j } , 0 \leq t \leq 2$ Suppose that $\int _ { C _ { 1 } } \vec { F } \cdot d \vec { r } = 5 , \int _ { C _ { 2 } } \vec { F } \cdot d \vec { r } = - 3$ and $\int _ { C _ { 3 } } \vec { F } \cdot d \vec { r } = - 3$ Evaluate g(2, -1).