Function Approximations Package Symbol

NIntegrateInterpolatingFunction

NIntegrateInterpolatingFunction[f, {x, x_min, x_max}]]
gives a numerical approximation to an integral with InterpolatingFunction objects in the integrand.

NIntegrateInterpolatingFunction[f, {x, x_min, x_max}, {y, y_min, y_max}, ...]
gives a numerical approximation to a multidimensional integral.

MORE INFORMATION

To use NIntegrateInterpolatingFunction, you first need to load the Function Approximations Package using Needs["FunctionApproximations`"].

NIntegrateInterpolatingFunction uses the function NIntegrate, but it breaks up the domain of integration into sections where the InterpolatingFunction objects are smooth.

If the integrand f does not contain any InterpolatingFunction objects, NIntegrateInterpolatingFunction is equivalent to NIntegrate.

The arguments of the InterpolatingFunction objects may themselves be univariate functions of the integration variables.

If the integrand f is simply an InterpolatingFunction object, it is better to use Integrate because this gives a result that is exact for the polynomial approximation used in the InterpolatingFunction object.

Numerically integrating a multidimensional integral using NIntegrateInterpolatingFunction with InterpolatingFunction objects containing a large number of nodes may take significantly longer than using NIntegrate.