Step 1 - Data and Initialization:

You have a numerical integration method and data points to compute an approximate integral.

Step 2 - Create a Romberg Table:

Build a Romberg integration table, which is a triangular table of values. The first column contains the results from applying the chosen numerical integration method with different step sizes.

Step 3 - Extrapolation:

Use Richardson extrapolation to fill in the rest of the table. The formula for the extrapolation is similar to the one previously explained for Richardson Extrapolation.

Step 4 - Convergence Check:

Assess the convergence by looking at the differences between adjacent values in the table.

Step 5 - Output:

The final value obtained after extrapolation from the Romberg table is an improved approximation of the definite integral.

Romberg integration is a method for improving the accuracy of numerical integration, particularly when the function is smooth but complex.