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516 APPENDIX A. MATHEMATICAL PRELIMINARIES
or ,
This result can be generalized as
(A.8-9)
where
b-a
n=1+- (A. 10)
8-
Ax
Simpson's rule
The trapezoidal rule fits a straight line (first-order polynomial) between the two
points. Simpson's rule, on the other hand, fits a second-order polynomial between
the two points. In this case the general formula is
where
b-a
n=- (A.8-12)
Ax
Note that this formula requires the division of the interval of integration into an
even number of subdivisions.
Example A.6 Determine the heat required to incme the temperature of benzene
vapor from 300 K to 1000 K at atmospheric pressure. The heat capacity of benzene
vapor varies as a function of temperature as follows:
