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Verify Green's Theorem for the line \int_C x d x + y d y, where C is the unit circle, oriented...

Question:

Verify Green's Theorem for the line {eq}\int_C x d x + y d y, {/eq} where C is the unit circle, oriented counterclockwise

Green's Theorem:

We will {eq}\oint F_{1}dx+F_{2}dy=\int \int \left ( \frac{\partial F_{2}}{\partial x}-\frac{\partial F_{1}}{\partial y} \right )dxdy {/eq} solve the problem using Green's Theorem here we will change the equation of circle to parametric form to solve the left side.

Answer and Explanation: 1

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To solve the problem we will use Green's Theorem:

{eq}\oint F_{1}dx+F_{2}dy=\int \int \left ( \frac{\partial F_{2}}{\partial x}-\frac{\partial...

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The Fundamental Theorem of Calculus

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Chapter 12 / Lesson 10
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The fundamental theorem of calculus is one of the most important points to understand in mathematics. Learn to define the formula of the fundamental theorem of calculus and explore examples of it put into practice.


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