## Integrating functions in Matlab

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integrate_functions

## 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.

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

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 =

0.3333



## double integrals

we use the dblquad command

Integrate over

i.e.

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

integrand =

-9.8696



## triple integrals

we use the triplequad command Integrate over the region

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

integrand =