In Section 2.1, the numerical method of random Gauss-Hermite for the evaluation of random

improper integrals is introduced and it is applied to an example strategically placed that will be used later in Section 3, where problem (1.1)-(1.2) is firstly analytically solved using the random Fourier transform.

And Section 3 is devoted to the definition of the Aumann fuzzy

improper integral. In Section 4, fuzzy Laplace transform is introduced, its basic properties are studied, and a particular case of Laplace convolution is investigated.

Secondly, we need to obtain the approximation of the

improper integral (15).

We think that this phenomenon was caused by the

improper integral constant, which makes us underestimate the IPS.

Moreover, suitable analytical acceleration techniques to fast evaluate the obtained

improper integrals of oscillating and slowly decaying functions has been developed.

provided this limit exists, and one says that the

improper integral converges in this case.

To see that the second integral in (3) converges, we use the comparison test for

improper integrals. Since f(t) is of exponential order 1/[k.sup.2], we have for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and hence:

Then the function [u.sub.1] given by the

improper integral (27) satisfies:

Then the

improper integral of first kind of the form [[infinity].sup.[infinity].sub.a] f(t)g(t)[DELTA]t is convergent.

Let us assume that the

improper integrals converge correctly and that we can keep a finite number of terms in the approximation of the integral:

creating an

improper integral. These properties of p.d.f.'s would

Maher); (60) Didactical Knowledge Development of Pre-Service Secondary Mathematics Teachers (Pedro Gomez and Luis Rico); (61) Legitimization of the Graphic Register in Problem Solving at the Undergraduate Level: The Case of the

Improper Integral (Alejandro S.