trapezoidal,simpson1/3,simpson3/8,booles.weddles,rectangular rules

1. University of Engineering & Technology LHR
(FAISALABAD CAMPUS) by FAISAL SAEED
Trapezoidal Rule
function trapezoidalrule
x0=input('Enter the value of initial input: ');
xn=input ('Enter the value of final input: ');
n=input ('Enter the total no of intervals : ');
h=(xn-x0)/n
f=input('Enter the function to be evaluated:');
sum=0;
for i=x0:h:xn
if(i==x0 || i==xn)
continue;
end
sum=sum +f(i);
end
sum=sum*2;
trapezoidal=h/2*(f(x0)+f(xn)+sum)
end

2. Output:-
Simpsons 1/3 Rule
function simpsonsrule
x0=input('Enter the value of initial input: ');
xn=input ('Enter the value of final input: ');
n=input ('Enter the total no of intervals : ');
h=(xn-x0)/n
f=input('Enter the function to be evaluated:');
sum=f(x0)+f(xn)+4*f(xn-h);
for count=1:2:n-3;
sum=sum+4*f(x0+count*h)+2*f(x0+(count+1)*h);
A=h*sum/3;
end
fprintf('integration is %d n ',A);
end

3. Output:-

4. Simpsons 3/8 Rule
function simpsonsrule
x0=input('Enter the value of initial input: ');
xn=input ('Enter the value of final input: ');
n=input ('Enter the total no of intervals : ');
h=(xn-x0)/n
f=input('Enter the function to be evaluated:');
sum=f(x0)+f(xn);
for count=1:n-1;
if (mod(count,3)==0)
sum=sum+2*f(x0+count*h);
else
sum=sum+3*f(x0+count*h);
end
end
A=sum*3*h/8;
fprintf('integration is %d n ',A);
end
Output:-

5. Booles Rule
function boolesrule
x0=input('Enter the value of initial input: ');
xn=input ('Enter the value of final input: ');
n=input ('Enter the total no of intervals : ');
h=(xn-x0)/n
f=input('Enter the function to be evaluated:');
sum=7*(f(x0)+f(xn))+32*f(xn-h);
for count=1:2:n-3;
sum=sum+32*f(x0+count*h)+12*f(x0+(count+1)*h);
A=2*h*sum/45;
end
fprintf('integration is %d n ',A);
end
Output:-

6. Weddles Rule
function weddlesrule
x0=input('Enter the value of initial input: ');
xn=input ('Enter the value of final input: ');
n=input ('Enter the total no of intervals : ');
h=(xn-x0)/n
f=input('Enter the function to be evaluated:');
sum=0;
sum1=0;
sum2=0;
for count=0:2:n;
sum=sum +f(count*h);
end
for count=1:4:n-1;
sum1=sum1+5*f(count*h);
end
for count=3:4:n-1;
sum2=sum2+6*f(count*h);
end
integrationis=3*h*(sum+sum1+sum2)/10
end

7. Output:-
Rectangular Rule
function rectangularrule
x0=input('Enter the value of initial input: ');
xn=input ('Enter the value of final input: ');
n=input ('Enter the total no of intervals : ');
h=(xn-x0)/n
f=input('Enter the function to be evaluated:');
sum=0;
for i=x0:h:xn
sum=f(i);
end
A=h*sum
end
Output:-