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For the numerical evaluation of univariate integrals over a finite interval the following strategy is used:
For multivariate integrals only the adaptive quadrature is used. This algorithm tolerates isolated singularities. The value \(iterations\) here limits the number of local interval intersection levels. \(Accuracy\) is a measure for the relative total discretization error (comparison of order 1 and order 2 approximations).
Syntax:
num_int
\((exp,var_1=(l_1 .. u_1)[,var_2=(l_2 .. u_2)\ldots ]\)
\([,accuracy=a][,iterations=i])\)
where \(exp\) is the function to be integrated,
\(var_1, var_2 , \ldots \) are the integration variables,
\(l_1, l_2 , \ldots \) are the lower bounds,
\(u_1, u_2 , \ldots \) are the upper bounds.
Result is the value of the integral.
Example:
num_int(sin x,x=(0 .. pi)); 2.0
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