How can i write this primitive function ?

How can i write the primitive function to this function I = x^N dx with an interval [0,1,]as an anonymous function and primitive function . AND How should I write a code that calculates exact integrals when N = 1, N = 2, N = 3, N = 4, N = 5. I wrote this kod but i do not know how to continue, iam getting an error which says "Unrecognized function or variable 'N' "

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

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

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

[Rik]

http://web.archive.org/web/20211216092212/https://www.mathworks.com/matlabcentral/answers/698685-how-can-i-write-this-primitive-function

Answer 1

[Alan Stevens]

You need to make the f's a function of N as well. e.g:

F=@(x,N)(x^((N)+1))/((N)+1);% Primitive function

then make sure you call them with two parameters. e.g:

F(b,N)

[Alan Stevens]

You probably want

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

[Rik]

Deleted comments:

Talia attq on 20 Dec 2020 (prior to the response by Alan):

now i wrote it this way

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

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

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

but I get the wrong values on exact value, cuz i calculated the values of its by hand and I got much less values than I got when I ran my matlab code

Talia attq on 20 Dec 2020

Thank you so much for the help

Talia attq on 20 Dec 2020

I have this numerical integrate 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

if i want to calculte the same function f= @(x,N)x.^N when N = 1, N = 2, N = 3, N = 4, N = 5, using my numerical integrate func 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 thinking about to writw tow for-loops.

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


exact_value = F(b,N)-F(a,N); % exact value
I=integrate(f, a, b, n);

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

for  N=1:5
    I(N)=integrate(f, a, b, n);
    
  for n=1:2
      I(n)=integrate(f, a, b, n);
      
  end
        
end

but when i ran it i got this error:

Error using /

Matrix dimensions must agree.

Error in integrate (line 3)

h =(b-a)/n;%interval size

Error in upp3b (line 8)

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

Answer 2

[Steven Lord]

f= @(x)x^N;%function
F=@(x)(x^((N)+1))/((N)+1);% Primitive function

Either define N before these two lines or define f and F to accept N as an additional input and pass both x and N into the function when you call it.

With either approach, because N is not a scalar, you'll need to use element-wise power and division operators .^ and ./ instead of ^ and /, see this documentation page.

But if you're not writing this as part of a homework assignment and you want to compute the integral of that function I recommend calling the integral function rather than writing your own.

[Steven Lord]

%{
exact_value = F(b,N)-F(a,N); % exact value
for i=1:length(N)   
exact_value = exact_value+(F(b,N)-F(a,N));
end

Nothing inside this for loop depends on the loop variable at all, so that code is equivalent to:

exact_value = (length(N)+1) * (F(b, N)-F(a, N));
%}

If you meant to add up all the elements of exact_value (as it was defined before the for loop) then either use sum or iterate over elements of exact_value.

exact_value = 1:5;
s1 = sum(exact_value)

s1 = 15

s2 = 0;
for whichValue = 1:numel(exact_value)
    s2 = s2 + exact_value(whichValue);
end
s2

s2 = 15

[Rik]

Deleted comments:

Talia attq on 20 Dec 2020

The problem is that i am writing this as a part of assignment, i wrote it this way now

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

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

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

but still it dosent work .I get the wrong values as exact value, cuz i calculated the values of its by hand and I got much less values than I got when I ran my matlab code

Talia attq on 20 Dec 2020

I have this numerical integrate 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

if i want to calculte the same function f= @(x,N)x.^N when N = 1, N = 2, N = 3, N = 4, N = 5, using my numerical integrate func 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 thinking about to writw tow for-loops.

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

but when i ran it i got this error:

Error using /

Matrix dimensions must agree.

Error in integrate (line 3)

h =(b-a)/n;%interval size

Error in upp3b (line 8)

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