# green

1. ### Green's theorem

I need a little help with the problem below: This is my issue with this question: I know the formula for Green's theorem. I worked through the problem and ended up with (-5/3). The answer was 5/3. The order of integration the lecturer used to solve the ensuing double integral was "dydx". I...
2. ### Green's Theorem

Where did y = 2x and y = x limits of integration come from? How could they be found using the vertices?
3. ### Green's Theorem

Let C be the positively oriented brink of the quarter-disk Q: 0 ≤ x 2 + y 2 ≤ 16, x ≤ 0, y ≤ 0. Calculate intg​c((x-y^3)dx+(y^3+x^3)dy))
4. ### Green's Theorem

Can it be used to evaluate all line integrals, or is it reserved for non-conservative ones?
5. ### Green's theorem excerpt

A bit of a vague question, but I can't understand what went on here. So we are integrating this over the three sides, which correspond to our curve in the counterclockwise direction. But the substitutions really confuse me. (Headbang) So in the first two integrals we walk our line of the...
6. ### Green Theorem - Question from Brazil

Hi everyone ! I have no idea how to solve this question that is in portuguese(I'm from Brazil). The translation is: Having the vectorial F and the relation : integrate F.dr = area of D , where D is a simple curve and like the Green theorem. Find the value of Beta(B) and the function f knowing...
7. ### Green's Theorem help

Hi, how would i start this question?, it doesn't look like any of the green's theorem forms I've seen (no dx in the formula). I presume I have to transform it into polar coordinates, can someone show how to do that with this particular question. Thanks.
8. ### Question on Green's theorem

Ok, I am completely stumped for this question, am I supposed to be using green's theorem for the first question (part a), if so there are three variables x y and z to use and I only learnt how to use green's theorem on two (dx dy). Can someone show me full steps to part a so I know how to answer...
9. ### Using Green's Theorem

My attempt: So obviously D is this triangle: And using Green's I get: [Double integral](δ/δx(e^y + (4x^3)(y^3) - yx) - δ/δy(xe^y + (3x^4)(y^2) - 3x - cosy^3)dA = [Integral from 0 to y][Integral from 0 to 1] (δ/δx(e^y + (4x^3)(y^3) - yx) - δ/δy(xe^y + (3x^4)(y^2) - 3x - cosy^3)dydx I'm not...
10. ### Solving wave equation using Green's function

I am currently self studying/ self teaching myself this great book Mathematical methods of physics by Mathews and Walker and must tell you that I am really struggling with the explanation of the solution of wave equation given on the book using Green's function from the start to the last, so...
11. ### Solve the given differential equation by using Green's function method

I am really struggling with the concept and handling of the Green's function. I have to solve the given differential equation using Green's function method \frac{d^{2}y}{dx^{2}}+k^{2}y=\delta (x-x');\qquad y(0)=y(L)=0
12. ### Green's Thm Problem

∫(2x+y^2(x))dx+(2xy+3y)dy where C is bounded by y=x^2+1, x+y=13 and x=1 with positive orientation

14. ### Green's theorem and line integral problem

Use Green's theorem to evaluate $\int_{C} 3xydx+2x^{2}dy$ Where C is the positively oriented boundary bounded by the parabola y=x^2 and y=-x I think I've got it set up right, but the end result is 0. Is that correct?
15. ### Green's Theorem problem

∫c (x^2+y^2)dx + (x^2+y^2)dy , C is defined by y=x , y=(1/6)x^2 , 0<x<6 For the limits I'm doing dydx, so: y is from 0 to x x is from 0 to 6 ∫c (x^2+y^2)dx + (x^2+y^2)dy = ∫∫2x-2y dydx = 2xy-y^2 from 0 to x = ∫x^2 dx = (1/3)x^3 from 0 to 6 = 72. I got it wrong... what did I do wrong and...
16. ### Green Theorem Help

The question is Use Green's Theorem to evaluate the integral below for the given path. ∫(y-x)dx+(7x-y)dy C: x = 4 cos(θ), y = sin(θ), 0 θ 2π I end up with ∫R∫ 6dydx but im stuck here. How do i setup the integral limits using the given Cubic Path? Thank you.
17. ### verify proof of Green's theorem

I have a question on Page 4 of the link you provided, the formula on the top of page 4:http://www.math.mcgill.ca/jakobson/courses/ma265/green.pdf \int_{c}\vec {F}\cdot(\hat {T}\times\hat {k})ds=\int_{c }(\hat {k} \times \vec {F})\cdot \hat {T} ds I want to verify how to get \int_{c} (\hat {k}...
18. ### weird hexagons and green thm

Hi, I would appreciate if someone could help. thanks. Calculate the work done by the non conservattive force F=x³j in moving a particle,around the regular hexagon with vertices at (√3,1),(0,2),(-√3,1),(-√3,-1),(0,-2) and (√3,-1) in that order. (use greens theorem). For this question I tried...
19. ### green theorem or stokes????

Hi,I dont think this is the normal integral. Please help with approach.thanks.i get confused btwn greens and stokes which is it? ∫(x²-2xy)dx+(x²y+3)dy where c is boundary of region defined by y^2=8x and x=2 traversed in counterclockwise direction. Thanks.
20. ### Green's Theorem Integration Question

Here's the question: So using Green's Theorem, I got that the integral is equal to \int_{C}\frac{\partial}{\partial x}(-e^xsiny) - \frac{\partial}{\partial x}(e^xcosy)dxdy = 0. But surely the answer can't be 0? What am I doing wrong? (Headbang)