Consider the Two-Dimensional Vector Field $\vec { F } ( x , y ) = - 4 y \vec { i } + 2 x \vec { j }$

Essay

Consider the two-dimensional vector field $\vec { F } ( x , y ) = - 4 y \vec { i } + 2 x \vec { j }$ Write down parameterizations of the three line segments C₁, C₂, and C₃ shown in the figure below. Use your parameterizations to compute the line integral $\int _ { C _ { 3 } + C _ { 2 } - C _ { 1 } } \vec { F } \cdot d \vec { r }$ by finding $\int_{G_{1}} \vec{F} \cdot d \vec{r}, \int_{C_{2}} \vec{F} \cdot d \vec{r}$ and $\int _ { C _ { 3 } } \vec { F } \cdot d \vec { r }$