How do i plot the integral against number points used?

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

[Rik]

So you want to sample the function and then integrate is, and plot the value of the integral as a function of the number of samples?

I have two points of advice: use linspace to create your list of points, it wil make sure you include your starting point and end-point in the number of steps needed, without you having to think about exceptions. The second point is that you can use trapz for numeric integration.

[Michael Lee]

I want to plot the integral of sin(x)^3 against the number of sample points used to evaluate that integral. If we choose n=20 (20 strips) then the number of sample points will be 21. So we evaluate the integral 21 times, first with n=1,2,3,4 ... 21

We should then get a value associated with each n+1 or no. of sample points used. I want to plot those.

Any ideas how i can do this?

[Rik]

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]

yeah thats perfect thank you

Answer 1

[Rik]

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)