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renolovexoxo
Posts: **2**Member

in Matlab

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);

% 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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