Unrecognized function or variable 'trapizoidal'.

%Matlab code for finding integration using different method

clear all

close all

% function for integration

f1=@(v) (5000.*v)./(8.276.*v.^2+2000);

%upper and lower limit

a=0; b=10;

%exact integral

ext_int=integral(f1,a,b);

%Function for which integration have to do

fprintf('\nFunction for which integration have to do f(v)=\n')

disp(f1)

fprintf('Upper and lower limit of integration [%2.2f %2.2f]\n\n',a,b)

fprintf('Exact integral for given function is %f\n',ext_int)

%Integration using Trapizoidal, Simpson 1/3 and Simpson 3/8 method

n=1;

val_trap=trapizoidal(f1,a,b,n);

err=(abs((val_trap-ext_int)/ext_int))*100;

fprintf('Relative percent Error in trapizoidal rule for n=%d is %f\n',n,err)

val_simp13=Simp13_int(f1,a,b,n);

err=(abs((val_simp13-ext_int)/ext_int))*100;

fprintf('Relative percent Error in Simpson 1/3 rule for n=%d is %f\n',n,err)

val_simp38=Simp38_int(f1,a,b,n);

err=(abs((val_simp38-ext_int)/ext_int))*100;

fprintf('Relative percent Error in Simpson 3/8 rule for n=%d is %f\n',n,err)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Integration using Trapizoidal, Simpson 1/3 and Simpson 3/8 method

n=20;

val_trap=trapizoidal(f1,a,b,n);

err=(abs((val_trap-ext_int)/ext_int))*100;

fprintf('Relative percent Error in trapizoidal rule for n=%d is %f\n',n,err)

val_simp13=Simp13_int(f1,a,b,n);

err=(abs((val_simp13-ext_int)/ext_int))*100;

fprintf('Relative percent Error in Simpson 1/3 rule for n=%d is %f\n',n,err)

val_simp38=Simp38_int(f1,a,b,n+1);

err=(abs((val_simp38-ext_int)/ext_int))*100;

fprintf('Relative percent Error in Simpson 3/8 rule for n=%d is %f\n',n+1,err)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%Matlab function for Trapizoidal integration

function val=trapizoidal(func,a,b,N)

% func is the function for integration

% a is the lower limit of integration

% b is the upper limit of integration

% N number of rectangles to be used

val=0;

%splits interval a to b into N+1 subintervals

xx=linspace(a,b,N+1);

dx=xx(2)-xx(1); %x interval

%loop for Trapizoidal integration

for i=2:length(xx)-1

xx1=xx(i);

val=val+dx*double(func(xx1));

end

val=val+dx*(0.5*double(func(xx(1)))+0.5*double(func(xx(end))));

fprintf('\t Integral using Trapizoidal method\n')

fprintf('The value of integral from a=%f to b=%f\n',a,b)

fprintf('using %d equally spaced divisions is : %2.15f\n',N,val)

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%Matlab function for Simpson 1/3 Method

function val=Simp13_int(f,a,b,n)

%f=function for which integration have to do

%a=upper limit of integration

%b=lower limit of integration

%n=number of subintervals

zs=f(a)+f(b); %simpson integration

%all x values for given subinterval

xx=linspace(a,b,n+1);

dx=(xx(2)-xx(1)); %x interval

%Simpson Algorithm for n equally spaced interval

for i=2:n

if mod(i,2)==0

zs=zs+4*f(xx(i));

else

zs=zs+2*f(xx(i));

end

end

%result using Simpson rule

val=double((dx/3)*zs);

fprintf('\t Integral using Simpson 1/3 method\n')

fprintf('The value of integral from a=%f to b=%f\n',a,b)

fprintf('using %d equally spaced divisions is : %2.15f\n',n,val)

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%Matlab function forSimpson 3/8 Method

function val=Simp38_int(f,a,b,n)

% f is the function for integration

% a is the lower limit of integration

% b is the upper limit of integration

% n is the number of trapizoidal interval in [a,b]

%splits interval a to b into n+1 subintervals

xx=linspace(a,b,n+1);

dx=(xx(2)-xx(1)); %x interval

val=f(a)+f(b);

%loop for trapizoidal integration

for i=2:n

if mod(i-1,3)==0

val=val+2*double(f(xx(i)));

else

val=val+3*double(f(xx(i)));

end

end

%result using midpoint integration method

val=(3/8)*dx*val;

fprintf('\n\t Integral using Simpson 3/8 method\n')

fprintf('The value of integral from a=%f to b=%f\n',a,b)

fprintf('using %d equally spaced divisions is : %2.15f\n',n,val)

end

%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%

[VBBV]

trapz function

https://www.mathworks.com/help/matlab/ref/trapz.html

[RenatoL]

I think it would be better if you save the functions trapizoidal, Simp13_int, and Simp38_int on separate .m files

Answer 1

[Alan Stevens]

This works for me exactly as you have listed it! This is the output:

Function for which integration have to do f(v)=

@(v)(5000.*v)./(8.276.*v.^2+2000)

Upper and lower limit of integration [0.00 10.00]

Exact integral for given function is 104.604010

Integral using Trapizoidal method

The value of integral from a=0.000000 to b=10.000000

using 1 equally spaced divisions is : 88.414202857547053

Relative percent Error in trapizoidal rule for n=1 is 15.477234

Integral using Simpson 1/3 method

The value of integral from a=0.000000 to b=10.000000

using 1 equally spaced divisions is : 58.942801905031367

Relative percent Error in Simpson 1/3 rule for n=1 is 43.651489

Integral using Simpson 3/8 method

The value of integral from a=0.000000 to b=10.000000

using 1 equally spaced divisions is : 66.310652143160283

Relative percent Error in Simpson 3/8 rule for n=1 is 36.607925

Integral using Trapizoidal method

The value of integral from a=0.000000 to b=10.000000

using 20 equally spaced divisions is : 104.567194078904976

Relative percent Error in trapizoidal rule for n=20 is 0.035196

Integral using Simpson 1/3 method

The value of integral from a=0.000000 to b=10.000000

using 20 equally spaced divisions is : 104.604038713787162

Relative percent Error in Simpson 1/3 rule for n=20 is 0.000027

Integral using Simpson 3/8 method

The value of integral from a=0.000000 to b=10.000000

using 21 equally spaced divisions is : 104.604063246835111

Relative percent Error in Simpson 3/8 rule for n=21 is 0.000051