532 Appendix A: Functions and Instructions
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 532 of 132
& (append) TI-89: ¥ p key TI-92 Plus: 2 H key
string1 & string2 ⇒ string
Returns a text string that is string2 appended
to string1.
"Hello " & "Nick" ¸
"He
ll
o Nic
k
"
‰() (integrate) 2<key
‰(expression1, var[, lower] [,upper]) ⇒ expression
‰(list1,var [,order]) ⇒ list
‰(matrix1,var [,order]) ⇒ matrix
Returns the integral of expression1 with
respect to the variable var from lower to upper.‰(x^2,x,a,b) ¸bò
3 -
aò
3
Returns an anti-derivative if lower and upper
are omitted. A symbolic constant of
integration such as C is omitted.
However, lower is added as a constant of
integration if only upper is omitted.
‰(x^2,x) ¸xò
3
‰(aùx^2,x,c) ¸aøxò
3 + c
Equally valid anti-derivatives might differ by
a numeric constant. Such a constant might be
disguised—particularly when an anti-
derivative contains logarithms or inverse
trigonometric functions. Moreover, piecewise
constant expressions are sometimes added to
make an anti-derivative valid over a larger
interval than the usual formula.
‰(1/(2ìcos(x)),x)!tmp(x) ¸
ClrGraph:Graph tmp(x):Graph
1/(2ìcos(x)):Graph ‡(3)
(2tanê(‡(3)(tan(x/2)))/3)
¸
‰() returns itself for pieces of expression1 that
it cannot determine as an explicit finite
combination of its built-in functions and
operators.
When lower and upper are both present, an
attempt is made to locate any discontinuities
or discontinuous derivatives in the interval
lower < var < upper and to subdivide the
interval at those places.
‰(bùe^(ëx^2)+a/(x^2+a^2),x)
¸
For the AUTO setting of the Exact/Approx
mode, numerical integration is used where
applicable when an anti-derivative or a limit
cannot be determined.
For the APPROX setting, numerical
integration is tried first, if applicable. Anti-
derivatives are sought only where such
numerical integration is inapplicable or fails.
‰(e^(ëx^2),x,ë1,1)¥¸ 1.493...