Derivation of Composition Formula for Evaluating Triple Integrals Numerically BY Using Trapezoidal rule and Midpoint and when the Singularity at both of End Integrals.

Abstract

The main aim of this paper to find values of the triple integration numerically which is improper
(singular) of the partial derivatives or improper at both of of the integration .
Also in this paper, we find general formula of the errors according behaviour of the integrands using
new approach is different from the previous approached by Mohammed [4] , Alttai [5] , Dayaa [6] and
others .
The RMTM method is a composition method of using trapezoidal on the dimension of y and
midpoint rule on the two dimensions interior x and exterior z with applying Romberg acceleration
method when the number of subintervals of interval of interior integral are equal to the number of
subintervals of exterior integral h  h  h  such that h is the distances between coordinates of x
and h is the distances between coordinates of y and h is the distances between coordinates of z
such that we can depend on it to calculate the triple integrations , and given higher accuracy in the
results by few subintervals and time less than the request time for the researchers in the same subject .