# Questions tagged [greens-theorem]

This tag is for questions about Green's theorem. Green's theorem gives the relationship between a line integral around a simple closed curve $C$ and a double integral over the plane region $D$ bounded by $C$.

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### Why is Stokes theorem not applicable / not used correctly in this case?

I am doing some exercises and I don't understand what is wrong with my solution here. The problem is: given the integral $$I = \int_S (1 + x^2) f(x) dydz - 2xy f(x) dz dx - 3z dx dy$$ Find such a ...
28 views

### Line Integral with absolute function

I'm trying to solve this line integral: $$\oint_{L} |x|dxdy$$ $$L: x^2 + y^2 = 1$$ So by dividing the domain into 2 half (left and right) and using Green's Theorem I can solve it. My question is when ...
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### Greene's Theorem On Triangular Region [closed]

$\int_C xy^2\mathrm{d}x + 2x^2y\mathrm{d}y ,$ C is the triangle with vertices (0,0), (2,2),(2,4) . My attempt : I drew the region And I'm taking orientation counterclockwise wise but now I'm not ...
22 views

### Balayage of delta measure at a point evaluated on fixed Borel set is a measurable function

I am trying to understand why if $G \subset \mathbb{C}$ is a bounded domain, and $\widehat{\mu}$ refers to the $\textbf{balayage}$ of the finite (positive) compactly supported measure (Borel measure) ...
1 vote
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### Work done by a field along a circle

I have the vector field $$F(x, y) = (\frac{-y}{(x-1)^2+y^2} + \frac{y}{(x+1)^2+y^2}, \frac{x-1}{(x-1)^2+y^2} + \frac{-x-1}{(x+1)^2+y^2})$$ Using Green's Theorem I want to calculate the work done by $F$...
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40 views

### Integral applying Green's Theorem

I have a vector field $\vec{F} = (-2y, x)$ and the curve $\{(x, y) : x^2+y^2 \leq 1; y > |x|\}$. Now I want to calculate the work done by the vector field along the curve that goes positively. So, ...
124 views

### Green's alternative formula for integration by parts

I'm currently implementing a method to solve usual elliptic problems where the classical form is the following: $$-\text{div}(k\nabla u) + \vec \beta \cdot \nabla u + \gamma u = f$$ Due to an ...
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