Numerical integration is a mathematical technique used to approximate the integral of a function when an exact solution is difficult or impossible to obtain analytically. This approach becomes essential in dealing with complex functions, where traditional analytical methods may fail due to issues like discontinuities or undefined behavior. It is particularly relevant when considering floating-point arithmetic and error analysis, as numerical integration often involves approximating values that can introduce errors. Additionally, this method is a key component in spectral methods, where integrals are computed to determine coefficients for approximating solutions to differential equations.
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