# Integral Approximations

#### renolovexoxo

I have this problem to do, involving estimating the error for the derivative as well as the Gaussian Approximation. I am having a lot of trouble figuring out if I can alter this code or if I have to write something new. This is the first time I've ever used MatLab, and I could use some help if anyone has any ideas. The assignment is attached. I used this, which was given in class, to do (ii)

% f(x), the function to integrate
% f= @(x) x^4-2*x ;
% f= @(x) exp(x);
f=@(x) sin(x);
% a, the lower limit of integration
a=0 ;
% b, the upper limit of integration
b=pi ;
% b=1.0;
% n, the number of segments. Note that this number must be even.
% n=20 ;
%************************************************* *********************
format long g
h=(b-a)/n ;
% Sum the odd index function values, and multiply by 4
sumOdd=0 ;
for i=1:2:n-1
sumOdd=sumOdd+f(a+i*h) ;
end
% Sum the even index function values, and multiply by 2
sumEven=0 ;
for i=2:2:n-2
sumEven=sumEven+f(a+i*h) ;
end
sum=4*sumOdd+2*sumEven+f(a)+f(b) ;
% Then multiply by h/3
approx=h/3*sum ;
%exact = quad(f,a,b) ;
%exact=exp(b)-exp(a);
exact=-cos(b)-(-cos(a));
error=abs(approx-exact);
disp(approx);
disp(exact);
disp(error);

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