HP 50g Graphing Integrate, ? Undefined, Lower limit, upper limit, integrand, name, Taylr, ∂, Σ

∫(Integrate)

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 –3 clear) returns a symbolic result. Some functions that the calculator can integrate include the following:

•All builtin functions whose antiderivatives can be expressed in terms of other builtin functions

— for example, SIN can be integrated since its antiderivative, COS, is a builtin function. The arguments for these functions must be linear.

•Sums, differences, and negations of builtin functi ons whose antiderivatives can be expressed in terms of other builtin functions — for example, 'S IN(X)–COS(X)'.

•Derivatives of all builtin functions — for example , 'INV(1+X^2)' can be integrated because it is the derivative of the builtin function ATAN.

•Polynomials whose base term is linear — for example, 'X^3+X^2–2*X+6' can be integrated since X is a linear term. '(X^2–6)^3+(X^2–6)^2' cannot be integrated since X^2–6 is not linear.

•Selected patterns composed of functions whose antiderivatives can be expressed in terms of

other builtin functions — for example, '1/(COS(X)* SIN(X))' returns 'LN(TAN(X))'.

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 –3 set) returns a numerical approximation, and stores the error of integration in variable IERR. ∫ consults the number format setting to determine how accurately to compute the result.

Access: …Á (Áis the rightshift of the Ukey).

Flags: Numerical Result (–3), Number Format (–45 to –50)

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 –3 clear) this command sequence:
	1 2 '10*X' 'X' „
	returns 15.
	In Numeric Results mode (flag –3 set) the above command sequence returns the numeric
	approximation 15.. In addition, the variable IERR is created, and contains the error of integration
	.00000000015.
See also:	TAYLR, ∂, Σ

?(Undefined)

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

3288 Full Command and Function Reference