C Integration Simpson's Rule - Texas Instruments TI-60 Owner's Manual

APPENDIX C
INTEGRATION : SIMPSON'S RULE
Integration : Simpson's Rule
Ttw integral key on the calculator uses Simpson's Rule, which is a method
of approximating the deflnte Integral of a function. An Integral can be
considered as the area under a curve
The area under the curve may be divided into an even number of
sublntervals. say 2n submtervals of length h - (b - a) -5- 2n with
endpoints x0 (-a), x,.x^.,. x*, (-b>
h
Ar " 3(y0 ♦
+ yj) is an approximation of the aera of R,
Similarly A, Is an approximation of R, Therefore A„ is an approximation of
the area of R„ Then adding A, + Aj + + A„ gives an approximation of
the area under the curve
This approximation lor definite integrals is stated in Simpson s rulo
I W*
- 3
%
♦ 4y, + 2 y, ♦ ♦ 2y^ - *V
t n ,
♦
Note that Ihe first and last terms in the parentheses have one for a
coefficient All olher -y terms with even subscripts have two for a
coefficient and all "y" terms with odd subscripts have four for a coefficient.
67-GB