The document describes MATLAB functions for numerical integration using various rules: 1) Trapezoidal, Simpsons 1/3, Simpsons 3/8, Booles, Weddles, and Rectangular rules are presented with code examples. 2) Each function takes the initial and final inputs, number of intervals, and function as inputs and returns the numerical integration as the output. 3) The functions break the interval into subintervals and calculate the area using the specific rule's formula to approximate the definite integral.

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:-