How to compute the double integral over dx and dy?

Hi, Can someone help me to how to code this equation in matlab? Let x and y are axis of a plane. dx and dy are increments. I have values of a and b at each coordinate(x,y) as shown in the below code.

clear all; close all;clc;

% Let
dx = 0.1;
x = -0.5:dx:0.5;

dy = 0.1;
y = -0.5:dx:0.5;

N = length(x);
a = randn(N,N);
b = randn(N,N);

Answer 1

[Star Strider]

You are integrating matrices, so use trapz (or cumtrapz, depending on the result you want) once in each dimension —

% clear all; close all;clc;

% Let
dx = 0.1;
x = -0.5:dx:0.5;

dy = 0.1;
y = -0.5:dx:0.5;

N = length(x);
a = randn(N,N);
b = randn(N,N);

columnInt = trapz((a-b).^2)                         % Column Integrals

columnInt = 1×11

19.6448 26.9404 10.3535 10.6369 19.7843 13.8794 7.4786 12.1139 10.1436 22.0933 19.0884

rowInt = trapz(columnInt)                           % Integrate Column Integrals

rowInt = 152.7905

totalInt = trapz((trapz((a-b).^2)))                 % Both In One Line

totalInt = 152.7905

.

[Torsten]

@Star Strider

Don't forget to scale the results by dx*dy.

[Star Strider]

I initially forgot that. Assuming ‘x’ defines the columns and ‘y’ defines the rows —

% clear all; close all;clc;

% Let
dx = 0.1;
x = -0.5:dx:0.5;

dy = 0.1;
y = -0.5:dx:0.5;

N = length(x);
a = randn(N,N);
b = randn(N,N);

columnInt = trapz(x,(a-b).^2)                         % Column Integrals

columnInt = 1×11

3.2512 1.1639 1.0265 1.5750 2.4845 1.1630 3.4526 2.8748 1.7902 0.9262 3.7454

rowInt = trapz(y,columnInt)                           % Integrate Column Integrals

rowInt = 1.9955

totalInt = trapz(y,trapz(x,(a-b).^2))                 % Both In One Line

totalInt = 1.9955

.

Answer 2

[Samyuktha]

Hi Kalasagarreddi,

I understand that you want to compute a double integral.

You can do this with the help of 'integral2' command. Please refer to the following documentation link for information on the syntax of 'integral2'.

integral2

Hope this helps!

Answer 3

[Torsten]

dx = 0.1;
x = -0.5:dx:0.5;
dy = 0.1;
y = -0.5:dx:0.5;
N = length(x);
a = randn(N,N);
b = randn(N,N);
F = (a-b).^2;
% Use one of the following approximations for the integral
I1 = trapz(y,trapz(x,F,2))

I1 = 2.0996

I2 = trapz(x,trapz(y,F,1))

I2 = 2.0996