One Dimensional Numerical Integration by Monte Carlo Method using Random and Equispaced Points

Abstract

Monte Carlo Method has taken extensive applications in many
fields using only random numbers generated by different and efficient
random number generators. The proposed research work deals with the
use of Monte Carlo Method for Numerical Integration. The basic
requirements for Monte Carlo method is Sample should be random and
Sample size should be large. So far the research work in this field only
comprises the efficiency of random number generator and how the
randomness of these numbers may be increased to get the best
approximation of an integral using these numbers. Here we are proposing
the same method for numerical integration but the approach takes a new
idea of using the equispaced numbers instead of random numbers i.e.
when we apply Monte Carlo method for numerical integration then
instead of evaluating the function over the random points in the given
range of integration we first divide the range of integration into n equal
interval, obtain n equispaced points and then evaluate the integral over
these points.