green's theorem

2022 1 9
2 个回答
更新时间：2024 11 23
27 次查看（30 天）

0 个投票

Verify Green’s theorem for the vector field𝐹=(𝑥2−𝑦3)𝑖+(𝑥3+𝑦2)𝑗, over the ellipse 𝐶:𝑥2+4𝑦2=64

6 个评论
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Rik
Rik 2022-1-16
Original question:
green's theorem
Verify Green’s theorem for the vector field𝐹=(𝑥2−𝑦3)𝑖+(𝑥3+𝑦2)𝑗, over the ellipse 𝐶:𝑥2+4𝑦2=64
Rena Berman
Rena Berman 2022-1-25

(Answers Dev) Restored edit

Rik
Rik 2022-2-2
@Sanjana Chhabra Why did you edit away your question again? That is very rude to Mehul, who was kind enough to spend time answering your question. Now you repay that kinding by making sure nobody else can benefit from that help.
Is this a homework assignment and are you afraid your instructor will find this question and accuse you of plagiarism?
Rena Berman
Rena Berman 2022-2-3

(Answers Dev) Restored edit

Gayathri
Gayathri 2023-7-8
integration [(xy+y^2)dx+(x^2)dy]
Walter Roberson
Walter Roberson 2023-7-8
@Gayathri I do not understand how that will help prove Green's theorem?
I am also unclear as to which variable the integration is with respect to?

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回答（2 个）

Mehul Mathur
Mehul Mathur 2022-1-11

1 个投票

clear
clc
syms x y t
F=input('Enter the vector function M(x,y)i+N(x,y)j in the form [M N]: ');
M(x,y)=F(1); N(x,y)=F(2);
r=input('Enter the parametric form of the curve C as [r1(t) r2(t)]: ');
r1=r(1);r2=r(2);
P=M(r1,r2);Q=N(r1,r2);
dr=diff(r,t);
F1=sum([P,Q].*dr);
T=input('Enter the limits of integration for t [t1,t2]: ');
t1=T(1);t2=T(2);
LHS=int(F1,t,t1,t2);
yL=input('Enter limits for y in terms of x: [y1,y2]: ');
xL=input('Enter limits for x as constants: [x1,x2]: ');
y1=yL(1);y2=yL(2);x1=xL(1);x2=xL(2);
F2=diff(N,x)-diff(M,y);
RHS=int(int(F2,y,y1,y2),x,x1,x2);
if(LHS==RHS)
disp('LHS of Greens theorem=')
disp(LHS)
disp('RHS of Greens theorem=')
disp(RHS)
disp('Hence Greens theorem is verified.');
end
Charles
Charles 2024-11-23
Ran in:

0 个投票

Ran in:
clear
clc
syms x y t
F=input('Enter the vector function M(x,y)i+N(x,y)j in the form [M N]: ');
Error using input
Support for user input is required, which is not available on this platform.
M(x,y)=F(1); N(x,y)=F(2);
r=input('Enter the parametric form of the curve C as [r1(t) r2(t)]: ');
r1=r(1);r2=r(2);
P=M(r1,r2);Q=N(r1,r2);
dr=diff(r,t);
F1=sum([P,Q].*dr);
T=input('Enter the limits of integration for t [t1,t2]: ');
t1=T(1);t2=T(2);
LHS=int(F1,t,t1,t2);
yL=input('Enter limits for y in terms of x: [y1,y2]: ');
xL=input('Enter limits for x as constants: [x1,x2]: ');
y1=yL(1);y2=yL(2);x1=xL(1);x2=xL(2);
F2=diff(N,x)-diff(M,y);
RHS=int(int(F2,y,y1,y2),x,x1,x2);
if(LHS==RHS)
disp('LHS of Greens theorem=')
disp(LHS)
disp('RHS of Greens theorem=')
disp(RHS)
disp('Hence Greens theorem is verified.');
end

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