What is Green's theorem: Definition and 134 Discussions

We can use Green's theorem to understand why the Exact Differential Equation satisfy the conditions it should have ... How about a DE for more than two variables ? Eg.dF=P(x,y,z,w)dx+Q(x,y,z,w)dy+R(x,y,z,w)dz+S(x,y,z,w)dw IF the equation above is an Exact Differential Equation , what...

any good notes/videos concerning green's theorem in plane? unfortunately missed my double lecture on it due to illness

Homework Statement Calculate the area of the region within x3 + y3 = 3xy. It can be parametrized by \gamma:[0,\infty] \rightarrow R2 with \gamma=<3t/1+t3, 3t2/1+t3>.Homework Equations Area = 1/2 \intx*dy - y*dx The Attempt at a Solution My plan is to take the curve parametrized by...

Homework Statement Use Green's theorem to compute the area of one petal of the 28-leafed rose defined by r = 5sin(14 \theta) Homework Equations A = \frac{1}{2} \int_c{x dy - y dx} \int \int_c{M_x + N_y}dx dy The Attempt at a Solution I'm really more confused about just what to do...

Homework Statement Solve: \oint x^{99}y^{100}dx + x^{100}y^{99}dy Assuming that it satisfies the conditions for Green's theroem, and: y = \sin{t} + 2, x = \cos{t}, 0 \leq t \leq 2\pi Homework Equations Green's theorem. The Attempt at a Solution \frac{\partial P}{\partial y} =...

Homework Statement Use Green's Theorem to calculate second type line integral: I = \oint_{\Gamma} x^2 y dx - xy^2dy where \Gamma[/tex] is the edge of domain D = \left\{(x,y) | x^2 + y^2 \leq 1, y \geq 0 \right\} Homework Equations Green's Theorem. The Attempt at a Solution Ok, so...

Homework Statement Use Green's theorem to compute the area of one petal of the 8-leafed rose defined by r=9sin(4theta) It may be useful for recall that the area of a region D enclosed by a curve C can be expressed as A =(1/2)int xdy-ydx. Homework Equations A =(1/2)int xdy-ydx The...

Homework Statement Evaluate: \int _C{xydx - yzdy + xzdz} C: \vec{r}(t) = t\vec{i} + t^2\vec{j} + t^4\vec{k} o <= t <= 1 Homework Equations The Attempt at a Solution I understand that you cannot use Green's Theorem in 3 dimensions. How else can I go about solving this?

Homework Statement Use Green's Theorem to calculate the circulation of \vec{G} around the curve, oriented counterclockwise. \vec{G} = 3y\vec{i} + xy\vec{j} around the circle of radius 2 centered at the origin. Homework Equations The Attempt at a Solution...

Homework Statement Given a curve C that starts from the origin, goes to (1,0) then goes to (0,1), then back to the origin, find the centroid of the enclosed area D. Homework Equations \bar{x} = {1/(2A)}*\int_C {x^2 dy}\bar{y} = -{1/(2A)}*\int_C {y^2 dx}The Attempt at a Solution Well, obviously...

Homework Statement Evaluate \displaystyle \int_C y^2dx + x^2dy for the path C: the boundary of the region lying between the graphs of \displaystyle y=x and \displaystyle y=\frac{x^2}{4}. Homework Equations The catch is that you can't use Green's Theorem. The Attempt at a Solution...

Homework Statement For a > 0, let C_a be the circle x^2 + y^2 = a^2 (counter-clockwise orientation). Let \textbf{F} : R^2 \ {0} \rightarrow R^2 be the following vectorfield: \textbf{F}\left(x,y\right) = F_1\left(x,y\right)\textbf{i} + F_2\left(x,y\right)\textbf{j} Also given...

Hi Everyone, Our class just learned Green's theorem using the Curl of a vector field F. I'm just having a tough time visualizing what in the world this means. I'm trying to view it in a physics perspective but I'm having a tough time. There's a picture in my textbook which has a plane with...

After much trouble with using the in-built engine to display all the mathematical formula, i thought scanning the question was the only way i could get my point across For (1) is C also defined by the parametric representation of \widetilde{}C which is why the direction of C is negative...

Homework Statement Hey. I need to use Green's theorem in order to solve this integral. My question is, how can I find the area for the Green's theorem integral? Homework Equations The Attempt at a Solution

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is...

As far as I know, Green's Theorem is normally stated for positively oriented curves (counterclockwise). If a curve is oriented clockwise, is it just the negative version? \oint Pdx + Qdy = - \int\int \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = \int\int \frac{\partial...

I have a problem from line integrals. My question is attached as a jpeg. Green's theorem is not valid for mine and i couldnot find a way. Pls take care of it.

Homework Statement is it possible to use green's theorem to derive the moment of inertia of solid objects? Homework Equations The Attempt at a Solution

Homework Statement http://www.geocities.com/asdfasdf23135/advcal26.JPG Note: path-connected means arcwise-connected C^0 means continuous ⊿f=Laplacian=(f)xx+(f)yy df/dn = grad f ． n 2. Relevant material Green's theorem, line integrals, ... The Attempt at a Solution The only part...

1) A vector form of Green's theorem states that under certain conditions, where n is the unit outward normal to the curve C and D is the region enclosed by C [Now, my question is: must n be a unit vector? Why or why not?] 2) A "regular region" is a compact set S in Rn that is the...

Homework Statement (Q) Find the outward flux of the field F=(3xy-x/(1+y^2 ))i+(e^x+tan^(-1)⁡y )j across the cardioid r=a(1+cos⁡θ), a>0. Homework Equations div F = (∂M )/∂x+∂N/∂y The Attempt at a Solution I could easily set up the double integral which is: ∬▒3 r^2...

Homework Statement Can someone please explain to me what the physical meaning of the divergence integrals and curl integral is? In the problems I have come across, they ask us to calculate areas and etc.. using Green's theorem. Which one should I use in that case? Thank-you very much for...

Please, give me idea about Green's theorem.

hi everybody, this is my first post, hope you can help me check this proof for Green's theorem for a particular case: http://en.wikipedia.org/wiki/Green%27s_theorem rigth after equation (3) you have to calculate the integral \int_{C_1} L(x,y)\, dx = \int_a^b...

Can someone help me with the following? I'm supposed to find the centroid of a region D using Green's Theorem. Assume that this density function is constant. ∫Pdx + ∫Qdy = ∫∫(dQ/dx)-(dP/dy) A = ∫xdy = -∫ydx = ½*∫xdy - ydx I know that the mass of a region D with constant density...

So a previous problem said to show that the area of some simple closed curve C was: A= \frac{1}{2} \oint_{C} (xdy - ydx) Simple enough. My problem says to find the area of the curve x^{2/3} + y^{2/3} = 4 using that formula. So off to polar coordinate land I go. r = 4, x = cos(t), dx =...

http://www.mrnerdy.com/forum_img/whichcorrect2.JPG which one is correct? [PLAIN]http://www.mrnerdy.com/forum_img/whichcorrect.JPG i tried both, and both gives different answer. one is 19/20 and another is 7/60

I'm having trouble on a line integral. Assuming that the closed curve C is taken in the counterclockwise sense. Use Green's Theorem. \int_C F\bullet dR where F=(x^2 + y^2)i + 3xy^2j and C is the circle x^2 + y^2 = 9 This is what I have done so far... \int_0^{2\Pi} \int_0^3 \-r^2...

find the double integral of the function e^(x^2) over the region where y/2 <= x<= 1 and 0<=y <=2 USING GREEN's THEOREM. I can't imagine how we'd use green's theorem here...if F=(P,Q) is the function, are we supposed to find P and Q using green's theorem and then parametrize the boundry of...

I'm giving a presentation on Green's theorm for class, and someone gave me this article that pretty much tells you how green's theorem work. It starts with 2 squares, and then you combine to square to form a rectangle, and then when you add the double integeral, line integeral, and the paths...

I find it a bit interesting that there is a separate theorem for Stokes theorem in a 2D situation. Can someone tell me why this is so? What's the history on these theorems. Did this guy Green come along and generalize Stokes theorem and get credit for it because if this is the case then I will...

K, I'm puzzled to death on a two problems involving Green's Theorem. They both are asking me to confirm that Green's theorem works for a given example, so I have to compute both the double integral over the area and the integral over the closed curve and make sure that they match.. only, on one...

Problem: Use Green's Theorem to evaluate the line integral: (integral over C) (2x dy - 3y dx) where C is a square with the vertices (0,2) (2,0) (-2,0) and (0, -2) and is transversed counterclockwise. Answer: will the double integral be -1 dydx? What will they go from? Will it be...