How do I do numerical integration of a vector in MATLAB?

Question

I have a vector of 358 numbers. I'd like to make a numerical integration of this vector, but I don't know the function of this one.

I found that we can use trapz or quad, but i don't really understand how to integrate without the function.

Answer 1

You don't need to know the function in order to numerically integrate; that's the point of trapz and quad. Just pass trapz your vector. http://www.mathworks.com/access/helpdesk/help/techdoc/ref/trapz.html

Answer 2

Think about integration as to find area under the curve, which is formed by your vector. Well it's not actually a curve, but polygonal chain. What TRAPZ function is doing, it finds sum of areas of each trapezoids formed by every two neighbor points in your vector and their projection on X axis. See the function documentation, if you have uneven distance between your points or if distance not equal one.

You can read more about this method, for example, on Wikipedia.

Answer 3

If you know the horizontal spacing of your vector, you can use trapz in order to integrate it without the function. For example, to integrate y=sin(x) from 0 to pi with 358 sections,

x=0:pi/357:pi;
y=sin(x);
area=trapz(x,y);

If you just use trapz(y), you'll get a much larger number, since the default distance between points is assumed to be 1. This problem can be fixed by multiplying by the distance between x points:

area=pi/357*trapz(y);