Numerical Integration

Numerical Analysis · Axiom Academy

Approximating definite integrals when exact solutions are impossible INTRO Why Numerical Integration? Many integrals cannot be evaluated analytically. Numerical integration (quadrature) approximates definite integrals using function values at discrete points. We approximate this by sampling f(x) at strategic points and combining the values with appropriate weights. Many important functions have no elementary antiderivative: Even when antiderivatives exist, they may be impractical to compute. Numerical methods provide accurate approximations efficiently. All numerical integration methods share a common form: We evaluate f at nodes x_0, x_1, ..., x_n and multiply by weights w_0, w_1, ..., w_n. Different methods choose different nodes and weights.

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