How can I integrate a function?

I have this numerical integration function:

function I = integrate(f, a, b, n)
h =(b-a)/n;%interval size
I=0;
for i=1:n %loop for the rest of the calculations
     p1 =(a+((i-1)*h)) + (h/4) ;
     m = ((a+((i-1)*h)) + (a+(i*h)))/2;
     p2 =(a+(i*h))- (h/4);
    I = I + (h/3)*((2*f(p1))-f(m)+(2*f(p2)));
    
end
    
end

I want to calculate the function f= @(x,N)x.^N when N = 1, N = 2, N = 3, N = 4, N = 5, using my numerical integration function I = integrate(f, a, b, n) . Two times : first when number of subintervals n=1, and the second time when n=2. How can I do this? I'm thinking about writing two for-loops.

x=a:1:b;
a =0;
b =1;
N=1:5;
n=1:2;
f= @(x,N)x.^N;%function
F=@(x,N)(x.^((N)+1))./((N)+1);% Primitive function


exact_value = F(b,N)-F(a,N); % exact value


int(N) = integrate(f(N),a,b, n);

for i=1:length(N)   
exact_value(i) =(F(b,N(i))-F(a,N(i)));
end


for j=1:length(N)
    int(j) = integrate (f(j),a,b,n);
    for k=1:length(n)
    int(k)=integrate(f, a, b,n(k));
    end 
end

but when I ran it I got this error:

Not enough input arguments.

Error in upp3b>@(x,N)x.^N (line 6)

f= @(x,N)x.^N;%function

Error in upp3b (line 13)

int(N) = integrate(f(N),a,b, n);

[Rik]

I recovered the removed content from the Google cache (something which anyone can do). Editing away your question is very rude. Someone spent time reading your question, understanding your issue, figuring out the solution, and writing an answer. Now you repay that kindness by ensuring that the next person with a similar question can't benefit from this answer.

http://web.archive.org/web/20211216091701/https://www.mathworks.com/matlabcentral/answers/698795-how-can-i-integrate-a-function

Answer 1

[Image Analyst]

You need to get the current value of N out of the N vector:

for j = 1 : length(N)
    thisN = N(j); % Extract this particular value of N
    int(j) = integrate (f(thisN), a, b, n);
    for k = 1 : length(n)
        int(k)=integrate(f, a, b, n(k));
    end 
end

[Rik]

Deleted comment:

a =0;
b =1;
N=1:5;
n=1:2;
f= @(x,N)x.^N;%function
F=@(x,N)(x.^((N)+1))./((N)+1);% Primitive function

exact_value = F(b,N)-F(a,N); % exact value

int= integrate(f(x,N),a,b, n);

for i=1:length(N)   
    exact_value(i) =(F(b,N(i))-F(a,N(i)));
end

for j=1:length(N)
    z = N(j); % Extract this particular value of N
    int(j) = integrate (f(x,z),a,b,n);
    for k=1:length(n)
    int(k)=integrate(f(x,N),a,b,n(k));
    end 
end

i ran it and got this error :

Error using .^

Matrix dimensions must agree.

Error in upp3b>@(x,N)x.^N (line 5)

f= @(x,N)x.^N;%function

Error in upp3b (line 12)

int= integrate(f(x,N),a,b, n);

Answer 2

[Jesús Zambrano]

You have defined 'f' as a function of x and N, but in the second for-loop and in the function 'integrate' you refer to 'f' with one argument instead of two.

[Rik]

Deleted comment:

a =0;
b =1;
N=1:5;
n=1:2;
f= @(x,N)x.^N;%function
F=@(x,N)(x.^((N)+1))./((N)+1);% Primitive function
exact_value = F(b,N)-F(a,N); % exact value
int= integrate(f(x,N),a,b, n);

for i=1:length(N)   
    exact_value(i) =(F(b,N(i))-F(a,N(i)));
end

for j=1:length(N)
    z = N(j); % Extract this particular value of N
    int(j) = integrate (f(x,z),a,b,n);
    for k=1:length(n)
    int(k)=integrate(f(x,N),a,b,n(k));
    end 
end

i ran it and got this error :

Error using .^

Matrix dimensions must agree.

Error in upp3b>@(x,N)x.^N (line 5)

f= @(x,N)x.^N;%function

Error in upp3b (line 12)

int= integrate(f(x,N),a,b, n);

Answer 3

[Image Analyst]

OK, not really sure what you're after but at least this runs without error. Put it all in one m-file.

% Initialization steps.  Brute force cleanup of everything currently existing to start with a clean slate.
clc;    % Clear the command window.
fprintf('Beginning to run %s.m ...\n', mfilename);
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;

a =0;
b =1;
x=a:1:b;
N=1:5;
n=1:2;
f = @(x,N) x.^N; % function
F = @(x,N) (x.^((N)+1))./((N)+1);% Primitive function

exact_value1 = F(b,N) - F(a,N); % exact value
% Looping way of doing the same thing.
for k = 1 : length(N)
	exact_value2(k) = F(b,N(k)) - F(a,N(k));
end

% int(N) = integrate(@f, a, b, N); % Won't work because N is a vector.

for j=1:length(N)
	thisN = N(j);
	int1(j) = integrate (f, a, b, thisN);
	for k=1:length(n)
		int2(k)=integrate(f, a, b, n(k));
	end
end
% Show values in the command window.
int1
int2

%=========================================================================
function I = integrate(f, a, b, n)
h = (b - a) / n; % interval size
I = 0;
for i = 1 : n % loop for the rest of the calculations
	p1 =(a+((i-1)*h)) + (h/4) ;
	m = ((a+((i-1)*h)) + (a+(i*h)))/2;
	p2 =(a+(i*h))- (h/4);
	I = I + (h/3)*((2 * f(p1, n)) - f(m, n) + (2 * f(p2, n)));
end

end