How can I do integral from discrete data points?

I have data "x" and "y" stored as arrays in MATLAB. How can I evaluate the area under the curve just from my data?

Answer 1

[MathWorks Support Team]

You can first interpolate your data to get a function handle. Then, you can use "integral" to integrate your data:

1. Create 50 sample data to work with

   >> n = 50;
   >> x = linspace(0, 2*pi, n);
   >> y = sin(x) + 0.1*randn(1,n);

 2. Plot the data to  visualize it

   >> plot(x,y,'x');

 3. Create an interpolation of the data, and save it as a function handle:

   >> F = griddedInterpolant(x,y);
   >> fun = @(t) F(t)

 4. Plot the function to visualize:

   >> plot(x, fun(x))

 5. Integrate the function with respect to x:

   >> q = integral(fun, x(1), x(end))