Integrate with Simpson's Rule

Question

Danny Helwegen 2019-1-13

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https://ww2.mathworks.cn/matlabcentral/answers/439604-integrate-with-simpson-s-rule

编辑： David Goodmanson 2019-1-14

Hi i have, probably an easy, problem. I made a function (see the outcome below) and i need to integrate the outcome, but since the interval is small the subscript indices aren't integers. This is the problem:

f =
    0.0028    0.1333    0.2667    0.4000    0.5333    0.6667    0.8000    0.9333    1.0667    1.1972

So then i use the Simpson Rule:

%interval is [0,1.2]
a = 0; b = 1.2; n =10; h = (b-a)/n
xi=a:h:b
I = h/3*(f(xi(1))+2*sum(f(xi(3:2:end-2)))+4*sum(f(xi(2:2:end)))+f(xi(end)));

But i get the error: Subscript indices must either be real positive integers or logicals.

How can I solve this?

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Answer 1

Matt J 2019-1-14

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https://ww2.mathworks.cn/matlabcentral/answers/439604-integrate-with-simpson-s-rule#answer_356254

编辑：Matt J 2019-1-14

在 MATLAB Online 中打开

It doesn't look like you xi should be involved, since you already have the samples of f

I = h/3*(f((1))+2*sum(f((3:2:end-2)))+4*sum(f((2:2:end)))+f((end)));

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David Goodmanson 2019-1-14

编辑：David Goodmanson 2019-1-14

Addressing f_i directly (assuming the x_i are equally spaced) is the right method, but the problem is that f has an even number of points. So the end point f(10) gets a weight of 5, not 1.

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