Numerical Integration

Sat, 24 Oct 2026 00:00:00 +0000

The Midpoint Rule

Approximate an integral by evaluating the function at the midpoint of each subinterval. The implementation below divides the interval into n equal parts.

def midpoint(f, a, b, n):
    if n < 1:
        raise ValueError("n must be positive")
    h = (b - a) / n
    return h * sum(f(a + (k + 0.5) * h) for k in range(n))

Divide the interval into equal parts.
Evaluate the function at the midpoint of each part.
Multiply the sum of those values by the step size.

Checking the Result

The midpoint estimates for the integral of x² on [0, 1] are:

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Mon, 01 Jan 0001 00:00:00 +0000

Unbloated Hugo Example

Numerical Integration

The Midpoint Rule

Checking the Result

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