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 $\int _ { C _ { 3 } } \vec { F } \cdot d \vec { r }$

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The Answer of 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 $\int _ { C _ { 3 } } \vec { F } \cdot d \vec { r }$

Consider the Two-Dimensional Vector Field F⃗(x,y)=−4yi⃗+2xj⃗\vec { F } ( x , y ) = - 4 y \vec { i } + 2 x \vec { j }F(x,y)=−4yi+2xj​

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