Let $\vec{F}$ and $\vec { G }$ be two 2-dimensional fields, where $\vec{F}=3 x \vec{i}+5 y \vec{j}$ and $\vec { G } = 3 y \vec { i } + 5 x \vec { j }$ Let C₁ be the circle with center (2, 2)and radius 1 oriented counterclockwise.
Let C₂ be the path consisting of the straight line segments from (0, 4)to (0, 1)and from (0, 1)to (3, 1).
Find the line integral $\int_{c_{2}} \vec{F} \cdot d \vec{r}$ Use "pi" to represent $\pi$ if necessary.

Question

Let

\vec{F}

and

\vec { G }

be two 2-dimensional fields, where

\vec{F}=3 x \vec{i}+5 y \vec{j}

and

\vec { G } = 3 y \vec { i } + 5 x \vec { j }

Let C₁ be the circle with center (2, 2)and radius 1 oriented counterclockwise.
Let C₂ be the path consisting of the straight line segments from (0, 4)to (0, 1)and from (0, 1)to (3, 1).
Find the line integral

\int_{c_{2}} \vec{F} \cdot d \vec{r}

Use "pi" to represent

\pi

if necessary.

Quizplus · Accepted Answer

The Answer of Let $\vec{F}$ and $\vec { G }$ be two 2-dimensional fields, where $\vec{F}=3 x \vec{i}+5 y \vec{j}$ and $\vec { G } = 3 y \vec { i } + 5 x \vec { j }$ Let C₁ be the circle with center (2, 2)and radius 1 oriented counterclockwise. Let C₂ be the path consisting of the straight line segments from (0, 4)to (0, 1)and from (0, 1)to (3, 1). Find the line integral $\int_{c_{2}} \vec{F} \cdot d \vec{r}$ Use "pi" to represent $\pi$ if necessary.

Let F⃗\vec{F}F And G⃗\vec { G }G Be Two 2-Dimensional Fields, Where F⃗=3xi⃗+5yj⃗\vec{F}=3 x \vec{i}+5 y \vec{j}F=3xi+5yj​

Let $\vec{F}$ And $\vec { G }$ Be Two 2-Dimensional Fields, Where $\vec{F}=3 x \vec{i}+5 y \vec{j}$