%Matlab code for finding integration using different
method
clear all
close all
%Probability distribution function
h=@(x) (1./(2.8.*sqrt(2*pi)))*exp((-(x-69).^2)/5.6);
%height between 65 to 70
a=65; b=70; n=2;
%Function for which integration have to do
fprintf('\nProbability distribution function h(x)=\n')
disp(h)
fprintf('Height between [%2.2f to %2.2f] is \n',a,b)
%Integration using Simpson 1/3 and Simpson 3/8 method
val_simp13=Simp13_int(h,a,b,n);
val_simp38=Simp38_int(h,a,b,n);
val_trap =trap_int(h,a,b,n);
fprintf('\tIntegration using Simpson 1/3 for 2 interval is
%f.\n',val_simp13)
fprintf('\tIntegration using Simpson 3/8 for 2 interval is %f.\n',val_simp38)
fprintf('\tIntegration using Trapizoidal method for 2 interval
is %f.\n',val_trap)
%height between 65 to 70
a=65; b=70; n=4;
%Function for which integration have to do
fprintf('\nProbability distribution function h(x)=\n')
disp(h)
fprintf('Height between [%2.2f to %2.2f] is \n',a,b)
%Integration using Simpson 1/3 and Simpson 3/8 method
val_simp13=Simp13_int(h,a,b,n);
val_simp38=Simp38_int(h,a,b,n);
val_trap =trap_int(h,a,b,n);
fprintf('\tIntegration using Simpson 1/3 for 4 interval is
%f.\n',val_simp13)
fprintf('\tIntegration using Simpson 3/8 for 4 interval is %f.\n',val_simp38)
fprintf('\tIntegration using Trapizoidal method for 4 interval
is %f.\n',val_trap)
%height between 65 to 70
a=65; b=1000; n=4000;
%Function for which integration have to do
fprintf('\nProbability distribution function h(x)=\n')
disp(h)
fprintf('Height greater than %d is \n',a)
%Integration using Simpson 1/3 and Simpson 3/8 method
val_simp13=Simp13_int(h,a,b,n);
val_simp38=Simp38_int(h,a,b,n);
val_trap =trap_int(h,a,b,n);
fprintf('\tIntegration using Simpson 1/3 for 4 interval is
%f.\n',val_simp13)
fprintf('\tIntegration using Simpson 3/8 for 4 interval is %f.\n',val_simp38)
fprintf('\tIntegration using Trapizoidal method for 4 interval is %f.\n',val_trap)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%Matlab function for mid point integration
function val=trap_int(f,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 Riemann integration
for
i=2:length(xx)-1
xx1=xx(i);
val=val+dx*double(f(xx1));
end
val=val+dx*(0.5*double(f(xx(1)))+0.5*double(f(xx(end))));
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);
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;
end
%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%
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