Let $\vec { F } = \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { i } + \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { j }$ For a fixed $\theta$ , let C _$\theta$ be the line segment from (0, 0)to the point (cos $\theta$ , sin $\theta$ )on the unit circle.
Find a parameterization of C _$\theta$ and compute $\int_{C_{0}} \vec{F} \cdot d \vec{r}$ .(Your answer will depend on $\theta$ .)

Question

Let

\vec { F } = \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { i } + \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { j }

For a fixed

\theta

, let C _$\theta$ be the line segment from (0, 0)to the point (cos

\theta

, sin

\theta

)on the unit circle.
Find a parameterization of C _$\theta$ and compute

\int_{C_{0}} \vec{F} \cdot d \vec{r}

.(Your answer will depend on

\theta

.)

Quizplus · Accepted Answer

The Answer of Let $\vec { F } = \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { i } + \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { j }$ For a fixed $\theta$ , let C _$\theta$ be the line segment from (0, 0)to the point (cos $\theta$, sin $\theta$)on the unit circle. Find a parameterization of C _$\theta$ and compute $\int_{C_{0}} \vec{F} \cdot d \vec{r}$ .(Your answer will depend on $\theta$ .)

Let F⃗=x2+y2i⃗+x2+y2j⃗\vec { F } = \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { i } + \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { j }F=x2+y2​i+x2+y2​j​

Let $\vec { F } = \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { i } + \sqrt { x ^ { 2 } + y ^ { 2 } } \vec { j }$