Derivation numericl method for evalution triple integral and its error formula by using trapezoidal method and mid point method

Abstract

Our main aim of this research is to derive new rule for evaluating triple integrals with continuous integrands by using trapezoidal and mid point rules and to  derive correction terms (error formula) and to improve the results by using Romberg  acceleration .we showed that the  composite method from Romberg  acceleration and the values yielded from mid point method at the exterior dimension(z) and trapezoidal method at the middle and interior dimension y and  x when the number  of subintervals  of exterior dimension equl to the number of subintervals of middle dimension and equl to the number of subintervals of interior dimension,that is,where as is the distances  on z ordinates, is the distances on y ordinates on and   is the distances on x ordinates  which we called it RMTT we can depend on it to evaluate triple integrals when the integrands are continuos and it gave high accuracy with little subinterrals