%  for
%   x^2
%   
clc;
clear all;
xb=1;
xe=3;
h=0.0001;
Sp=(xe^3-xb^3)/3
tic;
x=[xb:h:xe];
y=x.^2;
S=0;
for k=1:length(y)-1
  S=S+y(k);
end;
S=S*h
err=100*(S-Sp)/Sp
toc


%  for
%   x^2
%  
clc;
clear all;
xb=1;
xe=3;
h=0.0001;
Sp=(xe^3-xb^3)/3
tic;
x=[xb:h:xe];
y=x.^2;
S=0;
for k=1:length(y)-1
  S=S+y(k)+y(k+1);
end;
S=S*h/2
err=100*(S-Sp)/Sp
toc


%  while
%   x^2
%  
clc;
clear all;
xb=1;
xe=3;
h=0.0001;
Sp=(xe^3-xb^3)/3
tic;
x=[xb:h:xe];
y=x.^2;
S=0;
k=1;
while k <= length(y)-1
  S=S+y(k)+y(k+1);
  k=k+1;
end;
S=S*h/2
err=100*(S-Sp)/Sp
toc


%   sin(x)/x
%  
clc;
clear all;
xb=-16*pi;
xe=16*pi;
h=0.1;
tic;
x=[xb:h:xe];
y=sin(x)./x;
hold on;
plot(x,y);
for k=1:length(y)-1
  Sk=0;
  for n=1:k
    Sk=Sk+y(n)+y(n+1);
  end;
  Sk=Sk*h/2;
  S(k)=Sk;   
end;
x1=x(1,1:length(y)-1);
plot(x1,S,'-r');
grid on;
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