Gaussian quadrature is a numerical method used to approximate the definite integral of a function. It works by selecting specific points (called nodes) and weights to evaluate the function, allowing for an accurate estimation of the area under the curve. This technique is particularly effective for polynomial functions and can achieve high precision with fewer evaluations compared to traditional methods like the trapezoidal rule. The method is named after the mathematician Carl Friedrich Gauss, who contributed significantly to its development. Gaussian quadrature is widely used in various fields, including physics, engineering, and finance, where precise calculations of integrals are essential.