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Original Articles

Perfect numerical integration

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Pages 519-525 | Received 16 Jul 1985, Published online: 09 Jul 2006
 

In this paper, the general theory is presented for the class of functions which can be integrated exactly using a ‘reasonable symmetric quadrature formula’. It is shown that the class of functions which can be so integrated are antisymmetric about the mid‐point of the range of integration, and hence can be expressed as the sum of a constant and a function which is odd when viewed with respect to the mid‐point of this range. The value of the integral of such functions can be determined without the need to perform the integration.

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