Type: Function
Description: Integral Function: Integrates an integrand from lower limit to upper limit with respect to a specified variable of integration.
The algebraic syntax for ∫ parallels its stack syntax:
∫(lower limit, upper limit, integrand, name)
where lower limit, upper limit, and integrand can be real or complex numbers, unit objects, names, or algebraic expressions.
Evaluating ∫ in Symbolic Results mode (flag
•All
— for example, SIN can be integrated since its antiderivative, COS, is a
•Sums, differences, and negations of
•Derivatives of all
•Polynomials whose base term is linear — for example,
•Selected patterns composed of functions whose antiderivatives can be expressed in terms of
other
If the result of the integration is an expression with no integral sign in the result, the symbolic integration was successful. If, however, the result still contains an integral sign, try rearranging the expression and evaluating again, or estimate the answer using numerical integration.
Evaluating ∫ in Numerical Results mode (flag
Access: …Á | (Áis the |
Flags: Numerical Result
Input/Output:
|
| L4/A1 | L3/A2 | L2/A3 | L1/A4 |
| L1/I1 |
|
|
|
|
|
|
|
|
|
| lower limit | upper limit | integrand | 'name' | → | integral |
|
|
| 'symb ' | ||||
|
|
| L = Level; A = Argument; I = Item |
|
|
| |
Example: | In Symbolic Results mode (flag |
|
| ||||
| 1 2 '10*X' 'X' „ |
|
|
|
| ||
| returns 15. |
|
|
|
|
| |
| In Numeric Results mode (flag | ||||||
| approximation 15.. In addition, the variable IERR is created, and contains the error of integration | ||||||
| .00000000015. |
|
|
|
|
| |
See also: | TAYLR, ∂, Σ |
|
|
|
|
|
Type: Function
Description: The “undefined” symbol. Used to signify a numeric result that is not defined by the rules of arithmetic, such as the result of dividing zero by zero, or infinity by infinity. Mathematical operations on ? return ? as a result. Can be used in programs to check for an earlier undefined operation.
This use of ? is unrelated to the use of ? as a spare unit in the units system. The unit ? can be used to create new units based on it, units that can not be expressed in terms of other base units. For