MATLAB: Numerical integral at irregular intervals of scattered data

Question

I have two vectors x,y of equal size (for example 5000 elements), ranging from 0 to 1 (containing scattered data, but already sorted in increasing order). I want to evaluate the numerical integral of y(x) for each interval defined by the following vector [0 0.27 0.38 0.46 0.53 0.60 0.65 0.71 0.76 0.80 0.85 0.89 0.93 0.96 1] by means of trapz. How can I obtain the vector of evaluated integrals at each interval?

Answer 1

First use cumtrapz for cumulated integration, then use interp1 to interpolate to your vector:

z=cumtrapz(x,y);
zinter=interp1(x,z,xinter);

where xinter=[0 0.27 0.38 0.46 0.53 0.60 0.65 0.71 0.76 0.80 0.85 0.89 0.93 0.96 1]

Best wishes

Torsten.