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Use Stokes Theorem to find the line integral of \vec{F} = 4y\vec{i} + 3z\vec{j} +6x\vec{k}...

Question:

Use Stokes Theorem to find the line integral of {eq}\vec{F} = 4y\vec{i} + 3z\vec{j} +6x\vec{k}{/eq} around a circle {eq}C{/eq} of radius {eq}5{/eq} centered at {eq}(5,1,3){/eq} in the plane {eq}z = 3{/eq} oriented couterclockwise when viewed from above.

Line integral = {eq}\int_{C} \vec{F} d\vec{r}={/eq}

Finding the Line integral:

The objective is to find the line integral by using Stoke's theorem.

The general form of Stoke's theorem is {eq}\displaystyle \int_{C} F\cdot dr = \iint_{S} curl F\cdot n dS {/eq}

We have to find the area of the circle and apply in the general form to get a resultant part.

Answer and Explanation:

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The given function is {eq}\displaystyle \vec{F} = 4y \vec{i} + 3z \vec{j} + 6x \vec{k} {/eq}

The given plane is, {eq}\displaystyle z = 3 {/eq}.

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Work as an Integral

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Chapter 7 / Lesson 9
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After watching this video, you will be able to solve calculus problems involving work and explain how that relates to the area under a force-displacement graph. A short quiz will follow.


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