Page 421 - Excel for Scientists and Engineers: Numerical Methods

398 EXCEL: NUMERICAL METHODS

Integrates
Returns the integral (the area under the curve) of an expression between specified
limits. The area is calculated by using Simpson's 1/3 method.

Syntax
IntegrateS(expression, variable, from-lower, to-upper)
expression reference to a cell containing a formula (the integrand, the function
F(x)to be integrated)
variable cell reference corresponding to x, the variable of integration.
from-lo wer the lower limit of integration
to- upper the upper limit of integration

Remarks
The argument expression can be either a reference to a cell that contains a formula,
or a name.
The argument variable can be either a reference to a cell, or a name.
The arguments from-lower and to-upper can be either a number, a reference to a
cell containing a number, a formula or a name.
Errors (difference between returned value and correct value, when the latter can be
calculated using a calculus formula) are variable and depend on the expression
being integrated .
The area under the curve is divided into N "panels" of equal width H. The formula
for the area of each panel by Simpson's 1/3 rule is:
F(x) + 4F(x + HA) + F(x + H)
AH[ 3 1

Limitations
None of the precedent cells of the argument expression may contain references to
the argument reference.
The function cannot handle implicit references; that is, a name or range reference
cannot be used for a range of values.

Example
The formula =IntegrateS(C3,63,D3,E3), where C3 contains =B3"3, the expression to be
integrated, 63 is the variable of integration, D3 contains the value 0 and E3 the value 1,
returns the area under the curve of y = x3 between the limits 0 and 1.

See Also
CurvArea , Integrate, I ntegra teT