How do I compute a line integral of a function over a helix?

Question

Thien Son Phan 2018-4-3

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/392244-how-do-i-compute-a-line-integral-of-a-function-over-a-helix

评论： CARLOS RIASCOS 2018-4-3

在 MATLAB Online 中打开

So I need to find line the integral of

F=<(e^z)*(y^2), 2(e^z)xy, (e^z)x(y^2)> over a helix parametized as

x=2cost

y=2sint

z=t/5

for 0<= t <= 5pi.

I've no clue how to do this. I don't think I quite conceptually understand the requirement either.

Here's an attempt, however:

t=0:0.1:5*pi;
x=2.*cos(t);
y=2.*sin(t);
z=t./5;
myfunction =@(x,y,z) [(exp(z))*(y.^2); 2.*(exp(z)).*x.*y; (exp(z)).*x.*(y.^2)];
integral3(myfunction,-2,2,-2,2,0,pi);

Unfortunately, it did not work

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

CARLOS RIASCOS 2018-4-3

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/392244-how-do-i-compute-a-line-integral-of-a-function-over-a-helix#answer_313215

在 MATLAB Online 中打开

Hello brother, here is a code I did with symbolic mathematics using the mathematical definition of line integral with a vector field F. Postscript: The integral gives 0 LOL.

    syms t
    %Parametrization of the Curve:
    x=2*cos(t); y=2*sin(t); z=t/5;
    %Vector field:
    F = [exp(z)*(y^2), 2*exp(z)*x*y, exp(z)*x*(y^2)];
    %Dot product F*dr:
    D = F*[diff(x,t); diff(y,t); diff(z,t)];
    %Integral of line respect of t (dt):
    I = int(D,t,0,5*pi);
    i=double(I);
    %disp:
    disp('Value:')
    disp(i)

2 个评论
显示无隐藏无

Thien Son Phan 2018-4-3

Does MatLab actually produce 0 as an answer?

CARLOS RIASCOS 2018-4-3

Yes, It must be because the vector field F, is conservative, therefore its line integral on a closed curve in this case an ellipse is zero. But the code is fine, I tested it with exercises and the results of the code matched the results of the exercises. I hope my code will help you.

请先登录，再进行评论。