gives a numerical approximation to an integral with InterpolatingFunction objects in the integrand.
gives a numerical approximation to a multidimensional integral.
- To use , you first need to load the Function Approximations Package using Needs["FunctionApproximations`"].
- 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, 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 with InterpolatingFunction objects containing a large number of nodes may take significantly longer than using NIntegrate.
- has the same options as NIntegrate.
Since is not smooth, NIntegrate will generate a warning message:
In this case the integrand is simply an interpolating function, so you can use Integrate to check: