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Verify Green's theorem in the plane for \oint_C (x^3 - x^2y)dx + xy^2 dy, where C is the boundary...

Question:

Verify Green's theorem in the plane for {eq}\displaystyle \oint_C (x^3 - x^2y)dx + xy^2 dy {/eq}, where {eq}C {/eq} is the boundary of the region enclosed by the circles {eq}x^2 + y^2 = 4 {/eq} and {eq}x^2 + y^2 = 16 {/eq}.

Green's Theorem:

We will use Green's Theorem to solve the problem here the region lies in between the two circles whose radius is 2, 4 and center is (0,0) and we will use the polar coordinates to solve the problem.

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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