Formula:
The Trapezoidal Rule approximates the definite integral of a function f(x) over an interval [a, b] by dividing the area under the curve into a series of trapezoids. The formula is given by:
∫ab f(x) dx ≈ (h/2) [f(x0) + 2f(x1) + 2f(x2) + ... + 2f(xn-1) + f(xn)]
Where:
- f(x): The function to be integrated.
- a: The lower limit of integration.
- b: The upper limit of integration.
- n: The number of subintervals (trapezoids).
- h: The width of each subinterval, calculated as h = (b - a) / n.
- xi: The points along the x-axis, where x0 = a, xn = b, and xi = a + i · h.