Step 1 - Data and Initialization:

You have a definite integral to compute: ∫[a, b] f(x)dx, with n+1 equally spaced data points (x₀, f(x₀)), (x₁, f(x₁)), …, (x_n, f(x_n)).

Step 2 - Choose a Method and Subintervals:

Select a numerical integration method, such as the Composite Trapezoidal Rule or the Composite Simpson's Rule. Divide the interval [a, b] into n subintervals.

Step 3 - Apply the Chosen Method to Subintervals:

Use the selected method on each subinterval to approximate the integral. For the Composite Trapezoidal Rule, it's:

∫[a, b] f(x)dx ≈ h/2 [f(x₀) + 2∑(i=1 to n-1) f(x_i) + f(x_n)]

For the Composite Simpson's Rule, it's a more complex formula.

Step 4 - Evaluate Accuracy and Convergence:

Assess the accuracy of the composite numerical integration method by considering the error and comparing results obtained with different values of n (the number of subintervals).

Step 5 - Output:

The result of the chosen composite numerical integration method provides an approximation of the definite integral over the entire interval [a, b].

These methods are useful for approximating integrals when the function is not easily integrated analytically, especially when the interval of integration is long or the function varies significantly within the interval.