Texas Instruments TI-89 - Page 549

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)
¸
b
ò
3
-
a
ò
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)
¸
x
ò
3
‰(a
ù
x^2,x,c)
¸
a
ø
x
ò
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/(2
ì
cos(x)),x)
!
tmp(x)
¸
ClrGraph:Graph tmp(x):Graph
1/(2
ì
cos(x)):Graph ‡(3)
(2tan
ê
(‡(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.
‰(b
ù
e
^(
ë
x^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
^(
ë
x^2),x,
ë
1,1)
¥¸
1.493
...