Integration of a function with respect to a dummy variable

How to evaluate the integral ?

f(x) is integrated over a dummy variable z. Please note that x ((x(i) >= 0 or x(i) < 0)) is an array of n x 1 , and f(x) is a corresponding array of n x 1. I do not have the closed form expression for f(x), nor is curve fitting an option to approximate the data as an expression. How do I find corresponding vector A.

Kindly direct me to appropriate approach to solve this issue.

Answer 1

[Nikhil Yewale]

Hello

The issue is resolved by discussion with some friends

% say we are integrating a data resembling a parabola
x = -2:0.01:1;
y = x.^2;    
% say you wanted to integrate from x = -2 to x = 0..
% (lower limit x = -2 is variable..may use a loop over x as per user's req.)
index = find(x == 0);

I = cumtrapz(x(1:index),y(1:index)); 
% any ' i'th ' element in 'I' denotes integration from x = -2 to x = x(i)

-I(end)      % this should give integration of x.^2 from -2 to 0

Answer 2

[Hiro Yoshino]

Why don't you think about using Symblic Math Toolbox?

https://jp.mathworks.com/help/symbolic/index.html?s_tid=srchtitle

You can manipulate your equation as you wish.

[Nikhil Yewale]

Hello Sir, Thanks for the prompt reply

Symbolic toolbox is useful, however I do not have an expression for the function. I just have set of two arrays,

say x = [-0.5 -0.2 -0.1 -0.05 0 0.1 0.3 0.7] and so on

and I have corresponding array , say f = [-0.9 -0.5 0.4 0.3 0 -0.3 -0.5 0.5]

Using these two arrays I wish to find the integral , where you can imagine lower limit being set to 0, and upper limit being varied with each element of x(i).

This is like cumulative integral with a minor detail that lower limit is always set to 0.

Answer 3

[Hiro Yoshino]

f = [-0.9 -0.5 0.4 0.3 0 -0.3 -0.5 0.5]

let me assume z to be:

z = [0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0]

and

then

If you prefer continous manner, you should either approximate f as a function or interpolate the discrete numbers.

[Nikhil Yewale]

Thank you, Sir for your prompt reply,

I did get the idea that you were conveying from cumtrapz command and the issue is resolved.