!**********************************************************************!
!
! File: gauss5.f90 (29-Mar-2001)
!                  (24-Mar-2006)
!                  (20-Mar-2008)
!
! Numerische Integration der Funktion
!
!   f(x) = exp(x)
!
! mit der 5-Punkt Gauss-Legendre Formel
!
! a,b...Intervallgrenzen
!
!**********************************************************************!

module gauss5_m

!**********************************************************************!

  implicit none

  private

  integer,parameter,public::n=5
  real,dimension(n),parameter,public::w= &
       (/0.236927,0.478629,0.568889,0.478629,0.236927/)
  real,dimension(n),parameter,public::x= &
       (/-0.90618,-0.538469,0.0,0.538469,0.90618/)

  public::f

contains

!**********************************************************************!

  function f(x) result(y)

!**********************************************************************!

    real,intent(in)::x
    real::y

    y=exp(x)

  end function f

end module gauss5_m

!**********************************************************************!

program gauss5

!**********************************************************************!

  use gauss5_m

  implicit none

  integer::i
  real::a,b,s

  write(unit=*,fmt="(a)",advance="no") " a,b="
  read(unit=*,fmt=*) a,b

  s=0.0
  do i=1,n
    s=s+w(i)*f(0.5*(a+b+x(i)*(b-a)))
  end do
  s=0.5*(b-a)*s

  write(unit=*,fmt="(a,es14.7,a,es14.7,a)") " s=",s, &
       " (",exp(b)-exp(a),")"

end program gauss5

!**********************************************************************!