Numerical Integration Utility: Definite Integral of sin(x)
This page contains a routine that calculates the definite integral of sin(x) on an interval specified by the user.
Author: David K. Kahaner. Scientific Computing Division, NBS
From the book "Numerical Methods and Software" by
D. Kahaner, C. Moler, and S. Nash
Prentice Hall, 1988
To use this utility, the user must enter two values: b and c, which specify the range [b, c], over which
∫ sin(x) dx will be computed. b and c must be entered as radians, NOT degrees.
Note that over intervals for which the function is negative the integral is negative too. For example, the integral of this function from 0 to π is 2 while the integral of this function from π to 2 π is -2. Consequently, integrating this function over one complete cycle-- from x = 0 to x = 2 π --returns the result 2 + (-2) = 0.
IMPORTANT: Note the Error Code returned.
Error Code = 0: Normal Completion. e < eps (1.0E-12) and e < eps*abs(I).
Error Code = 1: Normal Completion. e < eps but e > eps*abs(I).
Error Code = 2: Normal Completion. e < eps*abs(I) but e > eps.
Error Code = 3: Normal completion but eps was too small to satisfy absolute or relative error request.
Error Code = 4: Aborted calculation because of serious rounding error. Probably e and I are consistent.
Error Code = 5: Aborted calculation because of insufficient storage. I and e are consistent.
Error Code = 6: Aborted calculation because of serious difficulties meeting error request.
Error Code = 7: More than 2*NMAX (= 100) iterations of main loop. Subroutine aborted.