PROGRAM trap1
!
! Author:  Br. David Carlson
!
! Date:  January 1, 2000
!
! Revised:  April 22, 2004
!
! This program finds the approximate value of the integral of sin(x) from
! 0 to pi.  The trapezoidal rule is used.

IMPLICIT NONE

INTEGER, PARAMETER::num = 100   ! Number of strips of area to sum up.
REAL::pi, delta, sum, area, x
INTEGER::k

! Function used:
REAL::f

WRITE (*, *) 'Program to integrate sin(x) from 0 to pi'

pi = 2.0 * ASIN(1.0)   ! Calculate pi.
delta = pi / num
x = delta
sum = (f(0.0) + f(pi)) / 2.0

DO k = 1, num - 1
   sum = sum + f(x)
   x = x + delta
END DO

area = delta * sum

WRITE (*, 100) area
100 FORMAT (1X, 'The trapezoidal rule gives an integral value of: ', E17.9)
WRITE (*, *) 'Of course, the exact value is 2.'

END PROGRAM


!  Given:   x   a real value
!  Task:    Compute f(x) and return it.
!  Return:  Computed value in function name.
REAL FUNCTION f(x)

IMPLICIT NONE

REAL, INTENT(IN)::x

f = SIN(x)
END FUNCTION