问题
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.
回答1:
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);
回答2:
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. Here's a link to the documentation.
回答3:
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.
来源：https://stackoverflow.com/questions/2861042/how-do-i-do-numerical-integration-of-a-vector-in-matlab