How do i plot the integral against number points used?

Question

Michael Lee 2017-3-15

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/330006-how-do-i-plot-the-integral-against-number-points-used

回答： Rik 2017-3-20

This currently the code i have for prompting the user for input for number of strips. I would like to be able to calculate the integral for n+1=1,2,3,4,5... and plot this against the sample points used. I dont have much of a clue on how to do this, i would suppose to use a for loop and then decrement the no of sample points used for each iteration.

Thanks, very new to matlab.

%Matlab script to evaluate the integral of sin^3(x) between 0 and pi/2
%Prompts the user for input number of strips
prompt = 'Please enter number of strips: ';
n = input(prompt);
%Declaration of constant and vectors
finish = pi/2;
h = finish/n;
points = 0:h:finish;  % From 0 to 'finish' with steps of 'h'
esno = 0;
osno = 0;
%Carry out the operator element wise, for each element
v = sin(points).^3;
% Loop for finding sum of even terms
for j = 2:2:n
    esno = esno + v(j);
end
% Loop for finding sum of odd terms
for k = 3:2:n-1
    osno = osno + v(k);
end
simpval = (h/3)*(v(1) + 4*esno + 2*osno + v(n+1))
%Graphing the convergence of integral with no. of sample points
samplepoints = n+1;
samplepointsvector = 1:1:samplepoints

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Rik 2017-3-15

在 MATLAB Online 中打开

I think I would do something like this:

total_samples=20;
integral_value=zeros(1,total_samples);
for n_samples=1:total_samples
  X=linspace(0,pi/2,n_samples+1);
  Y=sin(X).^3;
  integral_value(n_samples)=trapz(X,Y);
end
plot(1:total_samples,integral_value)

Please let me know if this is what you want, or explain how it doesn't do what you need.

Michael Lee 2017-3-20

yeah thats perfect thank you

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Answer 1

Rik 2017-3-20

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/330006-how-do-i-plot-the-integral-against-number-points-used#answer_259556

在 MATLAB Online 中打开

copied from comments

total_samples=20;
integral_value=zeros(1,total_samples);
for n_samples=1:total_samples
X=linspace(0,pi/2,n_samples+1);
Y=sin(X).^3;
integral_value(n_samples)=trapz(X,Y);
end
plot(1:total_samples,integral_value)