MatLab Integration Approximations for Given Function

  • Thread starter renolovexoxo
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In summary, this code is attempting to approximate the Simpson's rule integral using 20 equal intervals of length π/20.
  • #1
renolovexoxo
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Homework Statement


I need to answer the attached question, but we haven't done anything similar in class and the book isn't proving to be helpful for me. I'm not sure if I have to use matlab, we were given this code but I can't even understand what it is calculating.

% 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);

Any help would be greatly appreciated!
 

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  • #2
renolovexoxo said:

Homework Statement


I need to answer the attached question, but we haven't done anything similar in class and the book isn't proving to be helpful for me. I'm not sure if I have to use matlab, we were given this code but I can't even understand what it is calculating.

% 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);

Any help would be greatly appreciated!

It looks like a Simpson's rule approximation to the integral ##\int_0^{\pi} \sin(x) \, dx, ## using 20 equal intervals of length π/20. You are supposed also to compare the approximate and exact answers.

Note: I am not a Matlab user and so am unfamiliar with all the syntax and commands, etc., but it is more-or-less obvious what this code is attempting.

RGV
 
  • #3
Thank you for the help, but you don't need to make me feel bad for not understanding something you see is obvious. I do appreciate you pointing it out to me, I was having hard time seeing if it was the composite version.
 

1. What is MatLab Approximations?

MatLab Approximations is a feature in the MatLab software that allows users to estimate and approximate solutions to mathematical problems. It uses numerical methods and algorithms to provide a close approximation to the actual solution.

2. How accurate are the approximations in MatLab?

The accuracy of the approximations in MatLab depends on the specific problem and the chosen method of approximation. Generally, the accuracy increases as the number of iterations increases. However, it is important to note that these are approximations and may not always provide the exact solution.

3. What types of mathematical problems can be solved using MatLab Approximations?

MatLab Approximations can be used to solve a wide range of mathematical problems, including finding roots of equations, integration, differentiation, and solving differential equations. It can also be used for curve fitting and optimization problems.

4. How do I use MatLab Approximations?

To use MatLab Approximations, you need to have basic knowledge of MatLab programming language. You can access the approximations functions through the "approximations" menu in the MatLab interface. You will also need to input the necessary parameters, such as the initial guess and tolerance, for the specific problem you are trying to solve.

5. Can I trust the results from MatLab Approximations?

While MatLab Approximations can provide accurate results, it is important to always check and validate the results, especially for complex problems. It is also recommended to use multiple approximation methods and compare the results to ensure accuracy. Additionally, any errors or limitations in the initial guess or input parameters can affect the accuracy of the results.

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