PROGRAM integ3
!
! Author:  Br. David Carlson
!
! Date:  January 1, 2000
!
! Revised:  April 22, 2004; May 2, 2004; April 18, 2016
!
! This program finds the approximate value of the integral of ln(x + 1) from 1/4 to 3/4.
! The q1da.f library routine is used.

IMPLICIT NONE

REAL::area, A, B, error, EPS
INTEGER::KF, IFLAG

! Function used:
REAL::F

WRITE (*, *) 'Program to integrate ln(x + 1) from 1/4 to 3/4.'

A = 0.25
B = 0.75
EPS = 0.00001

CALL Q1DA(A, B, EPS, area, error, KF, IFLAG) 
!       A
!       B     (INPUT) THE ENDPOINTS OF THE INTEGRATION INTERVAL
!       EPS   (INPUT) THE ACCURACY TO WHICH YOU WANT THE INTEGRAL
!                COMPUTED.  IF YOU WANT 2 DIGITS OF ACCURACY SET
!                EPS=.01, FOR 3 DIGITS SET EPS=.001, ETC. 
!                EPS MUST BE POSITIVE. 
!       area  (OUTPUT) Q1DA'S BEST ESTIMATE OF YOUR INTEGRAL
!       error (OUTPUT) AN ESTIMATE OF ABS(INTEGRAL-area)
!       KF    (OUTPUT) THE COST OF THE INTEGRATION, MEASURED IN
!                   NUMBER OF EVALUATIONS OF YOUR INTEGRAND F.
!                   KF WILL ALWAYS BE AT LEAST 30.
!       IFLAG (OUTPUT) TERMINATION FLAG...POSSIBLE VALUES ARE 
!               0   NORMAL COMPLETION, error SATISFIES 
!                        error < EPS  AND  error < EPS * ABS(area)
!               1   NORMAL COMPLETION, error SATISFIES 
!                        error < EPS, BUT error > EPS * ABS(area)
!               2   NORMAL COMPLETION, error SATISFIES 
!                        error < EPS * ABS(area), BUT error > EPS 
!               3   NORMAL COMPLETION BUT EPS WAS TOO SMALL TO 
!                     SATISFY ABSOLUTE OR RELATIVE ERROR REQUEST.
! 
!               4   ABORTED CALCULATION BECAUSE OF SERIOUS ROUNDING
!                     ERROR.  PROBABLY error AND area ARE CONSISTENT. 
!               5   ABORTED CALCULATION BECAUSE OF INSUFFICIENT STORAGE. 
!                     area AND error ARE CONSISTENT. 
!               6   ABORTED CALCULATION BECAUSE OF SERIOUS DIFFICULTIES 
!                     MEETING YOUR ERROR REQUEST.  
!               7   ABORTED CALCULATION BECAUSE EPS WAS SET <= 0.0
! 
!            NOTE...IF IFLAG=3, 4, 5 OR 6 CONSIDER USING Q1DAX INSTEAD. 

WRITE (*, 100) area
100 FORMAT (1X, 'The q1da library routine gives an integral value of: ', E17.7)

WRITE (*, 200) error
200 FORMAT (1X, 'The error is estimated as: ', E17.7)

WRITE (*, 300) KF
300 FORMAT (1X, 'The cost is estimated as: ', I7)

WRITE (*, 400) IFLAG
400 FORMAT (1X, 'The IFLAG value is: ', I2)

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 = LOG(x + 1)
END FUNCTION