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function [I] = Simpson(x, y)
% Numerical evaluation of integral by Simpson's 1/3 Rule
% Inputs
% x = the vector of equally spaced independent variable
% y = the vector of function values with respect to x
% Outputs:
% I = the numerical integral calculated
%Error cheching
if length(x)~=length(y), error('The vectors need to be of equal lengths'),end
if length(x)==1, error('Vectors must be at least 2 data points long'),end
if range(x(2:end)-x(1:end-1))~=0, error('The x vector needs to be equally spaced'), end
%Error Errorchecking END
lower_bound=min(x);
interval=length(x)-1;
if rem(interval,2)==0
trap_rule=0;
upper_bound=max(x);
else
warning('Odd number of intervals. Applying Trapezoidal rule on last interval')
trap_rule=1;
upper_bound=x(end-1);
end
if length(x)==2
I=(upper_bound-lower_bound)*(y(1)+y(2))/2;
else
h=(upper_bound-lower_bound)/interval;
SumOdd=sum(y(1:2:end))-y(end-1);
SumEven=sum(y(2:2:end))-y(end-2);
I=(upper_bound-lower_bound)*(y(1)+4*SumOdd+2*SumEven+y(end))/(3*interval);
end
if trap_rule==1 & length(x)~=2
I_trap=(max(x)-upper_bound)*(y(upper_bound)+y(max(x)))/2;
I=I+I_trap;
end
end
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