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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Using Green's Theorem to find area

Hi, I'm little confused to use green's theorem for the area with using C1 and C2 curves. I tried to find the area by using polar coordinates but I ended up with a diverging integral. I calculated ...
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Understanding the line integral $\oint_c \vec{F} \cdot \,d\vec{r}$

I'd like to check my understanding of the following integral ( and hopefully, in the process, provide a page where other students can come to understand it as something other than a visual stimulus ...
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Using Green's Theorem to find area enclosed by curve

Use Green's theorem to calculate the area enclosed by the curve: $x^{2/3}+y^{2/3}=4$ Knowing that $A=\frac{1}{2}\int_c xdy-ydx$ I know that there are already some questions and answers on this ...
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green's theorem relating to calculating area

In this problem, I have to find the area of that blob. Pretty much I have to see if $\,N_x-M_y\,$ is equal to $1$. For the first choice, it is equal to $1$, yet the answer key says it is $4$?
Verify Green's thereom: $\oint_C (x^2 + y^2 +cos(x))dx +(x^2 +y^2 +sin(y))dy$ where C is the boundary of the semicircle" $${(x,y) \in R^2 :x^2 +y^2 \leq 4,x \geq 0 }$$ Solution: Please tell me ...
Evaluate $\int_{\gamma}xy\ dx$ where $\gamma$ is the boundary of the square with vertices $(0,0),(1,0),(1,1),(0,1)$. Now Green's Theorem says that $D$ be a bounded domain with piecewise ...