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Numerical Integration

Compute Compute ∫^{b}_{a} f(x) dx where f(x) is a given function. |

Numerical integration, also known as quadrature, is intrinsically a much more accurate procedure than numerical differentiation. Quadrature approximates the definite integral

by the sum

where the nodal abscissas x_{i} and weights A_{i} depend on the particular rule used for the quadrature. All rules of quadrature are derived from polynomial interpolation of the integrand. Therefore, they work best if f(x) can be approximated by a polynomial. ...

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