Integration by Monte Carlo Method 
by Reinaldo Baretti Machín
www.oocities.org/serienumerica
www.oocities.org/reibaretti2004
e-mail: reibaretti2004@yahoo.com



c     Integration of sin(x) by Monte Carlo method
c see solved problem 30.1 ,Numerical Analysis, Francis Scheid,
c     Schaum's Outline
      dimension na(400)
      real nmod
      f(x)=sin(x)
      pi=2.*asin(1.)
      nmod=2.**7
      x1=1.
      na(1)=int(x1)
      r=37.
      nsample=100
      kount=0
      sum=0.
      bmina=pi/2.-0.
      do 30 ii=1,nsample
      call aleat(x1,r,nmod,x2,naleat)
      theta=bmina*float(naleat)/nmod
      sum=sum+sin(theta)
      x1=x2
30    continue
      aint=  bmina*sum/float(nsample)
      print*,'aint,Iexact=',aint,1.
c      call alist (na,nsample)
      stop
      end
      

      subroutine aleat(x1,r,nmod,x2,naleat)
      real nmod
      x2=r*x1
      factor=x2/nmod
      x2=x2-int(factor)*nmod
      naleat=int(x2)
      x1=x2
      return
      end
      
      subroutine alist(na, nsample)
      dimension    na(400)
      in=ifix(float(nsample)/10.)
      nj1=1
      nj2=10*nj1
      Print*,'random numbers='
      do 10 i=1,in
      print*,(na(j),j=nj1,nj2)
      nj1=nj2+1
      nj2=10*(i+1)
10    continue
      return
      end
      
RUN
 aint,Iexact=  0.998798788  1.