compound trapezoidal integral
Divide the integration interval into small trapezoids to approximate the area.
symbols, variables and units
h=(b−a)/n: step size; n: number of segments; the error is related to the curvature of the function.
applicable conditions and boundaries
Equidistant nodes; overall error O(h²) when the second derivative is bounded.
formula source code
The following is a copyable LaTeX expression.
\int_a^b f(x)dx\approx h\left[\frac{f(a)+f(b)}2+\sum_{i=1}^{n-1}f(a+ih)\right]Reference and Extended Learning
Stanford · Convex Optimization, Boyd & Vandenberghe ↗is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.
trapezoidal rulenumerical integration