Page 420 - Excel for Scientists and Engineers: Numerical Methods

APPENDIX 3 CUSTOM FUNCTIONS HELP FILE 397

IntegrateT
Returns the integral (the area under the curve) of an expression between specified
limits. The area is calculated by using the trapezoidal approximation.

Syntax
I nteg rateT( expression, variable, from-lo wer, 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-lower 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 area of
each panel is approximated as the area of a trapezoid of width Hand heights F(x)
and F(x+H). The formula for the trapezoidal approximation is

2

Example
The formula =IntegrateT(C3,B3,D3,E3), where C3 contains =B3"3, the expression to be
integrated, B3 is the variable of integration, 03 contains the value 0 and E3 the value 1,
returns the area under the curve of y = x3 between the limits 0 and 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.

See Also
CurvArea, Integrate, Integrates