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+.help tintegrate Jan96 tables
+.ih
+NAME
+tintegrate -- Calculate the integral of one table column with
+respect to another.
+.ih
+USAGE
+tintegrate table integrand independent
+.ih
+DESCRIPTION
+The program evaluates the integral of the column name passed to
+'integrand' with respect to
+the column passed to 'independent' using the simple trapezoidal rule.
+The column passed to 'independent' must have values
+sorted in ascending order.
+INDEF values in either column are ignored, and there must be at least
+two good points common to both columns.
+The result is written to STDOUT and also recorded as a task parameter
+'integral'.
+
+If the 'independent' parameter is null or blank,
+the values in the 'integrand' column will simply be added up.
+Note that this is not exactly the same as the trapezoidal rule
+for integrating over row number.  (A row number column
+can be created using 'tcalc'.)  When integrating over a column
+that contains the row numbers,
+'tintegrate' adds together all rows except the first and last
+with unit weight;
+the first and last are included with a weight of one half.
+.ih
+PARAMETERS
+.ls table [file name]
+The input table.
+.le
+.ls integrand [string]
+Column name whose contents will be the integrand.
+.le
+.ls independent [string]
+Column name whose contents will be the independent variable;
+the values in this column must be increasing with row number.
+If 'independent' is null,
+then 'tintegrate' will just sum the values in the 'integrand' column.
+.le
+.ls (integral) [real]
+The result returned by the task.
+This is an output parameter; it is not directly changed by the user.
+.le
+.ls (ptsused) [integer]
+The number of points used in calculating the integral.
+This is also an output parameter and is not specified by the user.
+.le
+.ih
+EXAMPLES
+1.  Calculate the integral of flux over wavelength,
+printing the result to STDOUT
+(and also storing it in the 'integral' parameter).
+
+.nf
+tt> tintegrate intab flux lambda
+       integral= 0.8752311663155779 using 401 points
+.fi
+
+2.  Sum the values of flux, rather than integrating over wavelength.
+
+.nf
+tt> tintegrate intab flux ""
+       integral= 30.32557976245881 using 401 points
+
+as an alternative:
+
+tt> tstat intab flux
+# civ  flux
+# nrows            mean     stddev   median       min      max
+  401     0.07562488719   0.171107  -0.0381  -0.72729  0.22527
+tt> =0.07562488719 * 401
+30.32557976319
+
+.fi
+
+3.  Integrate the flux over row number.
+This is the same as summing the flux except for the first and last rows.
+
+.nf
+tt> tcalc intab row rownum datatype="real" colfmt="%8.1f"
+tt> tintegrate intab flux row
+      integral= 30.34466478228569 using 401 points
+.fi
+.ih
+BUGS
+.ih
+REFERENCES
+This task was written by David Giaretta.
+.ih
+SEE ALSO
+tcalc
+tstat
+.endhelp