Computing an specific numerical Integral

Question

Coo Boo 2020-2-8

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/504365-computing-an-specific-numerical-integral

编辑： Coo Boo 2020-2-8

采纳的回答： David Hill

Hi,

Can anyone help me in computing the following integral?

Thanks

2 个评论
显示无隐藏无

John D'Errico 2020-2-8

Homework?

Coo Boo 2020-2-8

编辑：Coo Boo 2020-2-8

Is it really so simple that it seems to be a homework? No, it's not really a homework. It is actually the first step in a research work. It is a fitness function that I have to optimize it through heuristic methods considering weights (wi) as the optimization variables.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

David Hill 2020-2-8

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/504365-computing-an-specific-numerical-integral#answer_414501

在 MATLAB Online 中打开

You could just expand the sumations since there are only 5.

fun=@(x)(.5*(1-x).^4+6*x.*(1-x).^3+4.5*x.^2.*(1-x).^2+4*x.^3.*(1-x)+.5*x.^4).*log(.5*(1-x).^4+6*x.*(1-x).^3+4.5*x.^2.*(1-x).^2+4*x.^3.*(1-x)+.5*x.^4);
y=integral(fun,0,1);

3 个评论
显示 1更早的评论隐藏 1更早的评论

David Hill 2020-2-8

在 MATLAB Online 中打开

You could play with somethng like this.

w=[.1 .3 .3 .2 .1];%size w will have to increase with n
fun=@(x,n)sum(reshape(cell2mat(arrayfun(@(y)w(y)*factorial(n)/factorial(y-1)/factorial(n-y).*x.^(y-1).*(1-x).^(n-y),1:n,'UniformOutput',false)),length(x),[]),2);
z=integral(@(x)fun(x,5).*log(fun(x,5)),0,1,'ArrayValued',true);%n=5

Coo Boo 2020-2-8

编辑：Coo Boo 2020-2-8

Thanks for your help.

请先登录，再进行评论。

Answer 2

Stijn Haenen 2020-2-8

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/504365-computing-an-specific-numerical-integral#answer_414506

I think you should use a Riemann integral to estimate the answer of this integral.

Or maybe wolfram Mathematica can solve it for you.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Coo Boo 2020-2-8

Thanks. But I need it in Matlab. Do you have any idea for solving it in Matlab with a 'for' loop or vectorized summation for any arbitrary n, e.g., n=100?

请先登录，再进行评论。