function I = trapezoidalRule(func,a,b,n)
h = (b-a)/n; % step size
F0 = func(a); Fn = func(b); %first and last elements
x = a;
sigma = 0;
for k=1:n-1
x = x+h;
sigma = sigma + func(x); % sum of intermediate elements
end
I = (h/2)*(F0+ 2*sigma + Fn); %final integral approximation
end
---------------------------------------------------------
function I = simpsonsRule(func,a,b,n)
h = (b-a)/n; %step size
F = 0;
for i=0:n
if i==0 || i==n % first and last coefficients
c =1;
elseif mod(i,2)~=0 %odd coefficients
c = 4;
elseif mod(i,2)==0 %even coefficients
c = 2;
end
F = F + c*func(a+i*h); % computing the sum
end
I = (h/3)*F; % final integral approximation
end
---------------------------------------------------------------
%driver file
clear
clc
% Task 1
func = @(x) 3 + (x.*sin(x))./(x-1);
a = 2; b = 7; n = 9;
% using trapezoidal rule
Itrap = trapezoidalRule(func,a,b,n)
% using simpson's rule
Isimp = simpsonsRule(func,a,b,n)
% using quad function
Iquad = quad(func,a,b)
%percentage error
ItrapPercentError = (abs(Iquad-Itrap)/Iquad)*100
IsimpPercentError = (abs(Iquad-Isimp)/Iquad)*100
%--------------------------------------------------------------
% Task 2
func = @(x) 6 + 3.*cos(x);
a = 0; b = pi/2;
disp('1 - composite trapezoidal rule')
disp('2 - composite simpson''s 1/3 rule')
rule = input('Which rule to use? ');
n = input('Enter number of points n: ');
if n>=2
switch rule
case 1
Itrap = trapezoidalRule(func,a,b,n)
Iquad = quad(func,a,b)
%percentage error
ItrapPercentError = (abs(Iquad-Itrap)/Iquad)*100
case 2
Isimp = simpsonsRule(func,a,b,n)
Iquad = quad(func,a,b)
IsimpPercentError = (abs(Iquad-Isimp)/Iquad)*100
otherwise
disp('invalid input')
end
else
disp('invalid number of points')
end
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