## 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.

**References:**

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

The original sub-routines were written in FORTRAN and have been translated to Javascript here. Although all care has been taken to ensure that the sub-routines were translated accurately, some errors may have crept into the translation. These errors are mine; the original FORTRAN routines have been thoroughly tested and work properly. Please report any errors to the webmaster.

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.