Integrating functions in Matlab

August 01, 2011 at 06:12 PM | categories: basic matlab | View Comments

integrate_functions

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Integrating functions in Matlab

it is a good idea to add these lines to the top of your m-files. They keep things looking neat!

close all  % close all figure windows that are open
clear all  % clear all the variables currently stored in memory
clc        % clear the commands in the command window

Problem statement

find the integral of a function f(x) from a to b i.e.

$$\int_a^b f(x) dx$$

In matlab we use numerical quadrature to achieve this with the `quad` command. f = @(x) some_function_of_x quad(f,a,b)

as a specific example, lets integrate

$$y=x^2$$

from x=0 to x=1. You should be able to work out that the answer is 1/3.

f = @(x) x.^2;  %note we must use .^ to ensure element-wise squaring
a = 0;
b = 1;

integrand = quad(f,a,b)

integrand =

    0.3333

double integrals

we use the `dblquad` command

Integrate $f(x,y)=y sin(x)+x cos(y)$ over

$\pi <= x <= 2\pi$

$0 <= y <= \pi$

i.e.

$\int_{x=\pi}^{2\pi}\int_{y=0}^{\pi}y sin(x)+x cos(y)dydx$

f = @(x,y) y*sin(x)+x*cos(y);
x1=pi; x2=2*pi;
y1=0; y2=pi;
integrand = dblquad(f, x1,x2,y1,y2)

integrand =

   -9.8696

triple integrals

we use the `triplequad` command Integrate $f(x,y,z)=y sin(x)+z cos(x)$ over the region

$0 <= x <= \pi$

$0 <= y <= 1$

$-1 <= z <= 1$

f = @(x,y,z) y*sin(x)+z*cos(x);
x1=0; x2=pi;
y1=0; y2=1;
z1=-1; z2=1;
integrand = triplequad(f, x1,x2,y2,y2,z1,z2)

% categories: Basic matlab
% tags: math

integrand =

     0


Published with MATLAB® 7.10

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