PROGRAM series15
!
! Author:  Br. David Carlson
!
! Date:  December 31, 1999
!
! Last Revised:  May 2, 2004
!
! This program uses Taylor series to find an approximate value for the
! integral of sin(x) from 0 to pi.  Compare with the output of integ3.f90.
! Of course, a series approximation is unnecessary, as is any numerical
! approximation, since the exact answer is known from calculus as 2.

IMPLICIT NONE

REAL::x, xsquared, term, sum

WRITE (*, 20)
20 FORMAT (1X, 'Program to integrate sin(x) from 0 to pi using series')

x = 2.0 * ASIN(1.0)   ! Calculate the value of pi.
sum = 0.0
xsquared = x * x
term = xsquared

sum = sum + term / 2.0
term = term * xsquared
sum = sum - term / 24.0
term = term * xsquared
sum = sum + term / 720.0
term = term * xsquared
sum = sum - term / 40320.0

WRITE (*, 200) sum
200 FORMAT (1X, 'The approximate value is ', E16.8)

END PROGRAM