Python:实现numerical integration数值积分算法(附完整源码)

from __future__ import annotations

from collections.abc import Callable


def trapezoidal_area(
    fnc: Callable[[int | float], int | float],
    x_start: int | float,
    x_end: int | float,
    steps: int = 100,
) -> float:

  
    x1 = x_start
    fx1 = fnc(x_start)
    area = 0.0

    for i in range(steps):

        # Approximates small segments of curve as linear and solve
        # for trapezoidal area
        x2 = (x_end - x_start) / steps + x1
        fx2 = fnc(x2)
        area += abs(fx2 + fx1) * (x2 - x1) / 2

        # Increment step
        x1 = x2
        fx1 = fx2
    return area


if __name__ == "__main__":

    def f(x):
        return x**3

    print("f(x) = x^3")
    print("The area between the curve, x = -10, x = 10 and the x axis is:")
    i = 10
    while i <= 100000:
        area = trapezoidal_area(f, -5, 5, i)
        print(f"with {i} steps: {area}")
        i *= 10

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