# How do I integrate a discrete function in MATLAB?

Many students ask me how do I do this or that in MATLAB.  So I thought why not have a small series of my next few blogs do that.  In this blog, I show you how to integrate a discrete function.

The MATLAB program link is here.

The HTML version of the MATLAB program is here.

_____________________________________________________

%% HOW DO I DO THAT IN MATLAB SERIES?
% In this series, I am answering questions that students have asked
% me about MATLAB.  Most of the questions relate to a mathematical
% procedure.

%% TOPIC
% How do I integrate a discrete function?  Three cases of data are
% discussed.

%% SUMMARY

% Language : MATLAB 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://nm.mathforcollege.com/blog/integrationdiscrete.m;
% Last Revised : April 3, 2009;
% Abstract: This program shows you how to integrate a given discrete function.

clc
clear all

%% INTRODUCTION

disp(‘ABSTRACT’)
disp(‘   This program shows you how to integrate’)
disp(‘   a discrete function’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar K Kaw of http://autarkaw.wordpress.com’)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://nm.mathforcollege.com/blog/integrationdiscrete.m’)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   April 3, 2009’)
disp(‘ ‘)

%% CASE 1

%% INPUTS

% Integrate the discrete function y from x=1 to 6.5
% with y vs x data given as (1,2), (2,7), (4,16), (6.5,18)
% Defining the x-array
x=[1  2  4  6.5];
% Defining the y-array
y=[2  7  16  18];

%% DISPLAYING INPUTS
disp(‘____________________________________’)
disp(‘CASE#1’)
disp(‘LOWER LIMIT AND UPPER LIMITS OF INTEGRATION MATCH x(1) AND x(LAST)’)
disp(‘ ‘)
disp(‘INPUTS’)
disp(‘The x-data is’)
x
disp(‘The y-data is’)
y
fprintf(‘  Lower limit of integration, a= %g’,x(1))
fprintf(‘\n  Upper limit of integration, b= %g’,x(length(x)))
disp(‘ ‘)

%% THE CODE

intvalue=trapz(x,y);

%% DISPLAYING OUTPUTS

disp(‘OUTPUTS’)
fprintf(‘  Value of integral is = %g’,intvalue)
disp(‘  ‘)
disp(‘___________________________________________’)

%% CASE 2

%% INPUTS

% Integrate the discrete function y from x=3 to 6
% with y vs x data given as (1,2), (2,7), (4,16), (6.5,18)
% Defining the x-array
x=[1  2  4  6.5];
% Defining the y-array
y=[2  7  16  18];
% Lower limit of integration, a
a=3;
% Upper limit of integration, b
b=6;
%% DISPLAYING INPUTS

disp(‘CASE#2’)
disp(‘LOWER LIMIT AND UPPER LIMITS OF INTEGRATION DO not MATCH x(1) AND x(LAST)’)
disp(‘  ‘)
disp(‘INPUTS’)
disp(‘The x-data is’)
x
disp(‘The y-data is’)
y
fprintf(‘  Lower limit of integration, a= %g’,a)
fprintf(‘\n  Upper limit of integration, b= %g’,b)
% Choose how many divisions you want for splining from a to b
n=1000;
fprintf(‘\n  Number of subdivisions used for splining = %g’,n)
disp(‘  ‘)
disp(‘  ‘)

%% THE CODE

xx=a:(b-a)/n:b;
% Using spline to approximate the curve from x(1) to x(last)
yy=spline(x,y,xx);
intvalue=trapz(xx,yy);

%% DISPLAYING OUTPUTS

disp(‘OUTPUTS’)
fprintf(‘  Value of integral is = %g’,intvalue)
disp(‘  ‘)
disp(‘___________________________________________’)
%% CASE 3

%% INPUTS

% Integrate the discrete function y from x=1 to 6.5
% with y vs x data given as (1,2), (4,16), (2,7), (6.5,18)
% The x-data is not in ascending order
% Defining the x-array
x=[1  4   2 6.5];
% Defining the y-array
y=[2  16  7 18];
% Lower limit of integration, a
a=3;
% Upper limit of integration, b
b=6;
%% DISPLAYING INPUTS

disp(‘CASE#3’)
disp(‘LOWER LIMIT AND UPPER LIMITS OF INTEGRATION DO not MATCH x(1) AND x(LAST) ‘)
disp(‘AND X-DATA IS NOT IN ASCENDING OR DESCENDING ORDER’)
disp(‘   ‘)
disp(‘INPUTS’)
disp(‘The x-data is’)
x
disp(‘The y-data is’)
y
fprintf(‘  Lower limit of integration, a= %g’,a)
fprintf(‘\n  Upper limit of integration, b= %g’,b)
% Choose how many divisions you want for splining from a to b
n=1000;
fprintf(‘\n  Number of subdivisions used for splining = %g’,n)
disp(‘  ‘)
disp(‘  ‘)

%% THE CODE
[x,so] = sort(x); % so is the sort order
y = y(so); % y data is now in same order as x data
xx=a:(b-a)/n:b;
% Using spline to approximate the curve from x(1) to x(last)
yy=spline(x,y,xx);
intvalue=trapz(xx,yy);

%% DISPLAYING OUTPUTS

disp(‘OUTPUTS’)
fprintf(‘  Value of integral is = %g’,intvalue)
disp(‘  ‘)

____________________________________________________________

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://nm.mathforcollege.com/videos

## 0 thoughts on “How do I integrate a discrete function in MATLAB?”

1. The above integration scheme for discrete function is very useful for physicsists. For example, in characterizing the spectrum of x-ray diffraction, which it’s data are always available in discrete forms. Thanks for your explanation.

2. The above integration scheme for discrete function is very useful for physicsists. For example, in characterizing the spectrum of x-ray diffraction, which it’s data are always available in discrete forms. Thanks for your explanation.

3. sagar says:

sir can u please teach us double integration for discrete function having three matrices x, y,and z.

4. sagar says:

sir can u please teach us double integration for discrete function having three matrices x, y,and z.