Texas Instruments Titanium TI-89, User Manual

Page: 883 / 977

880 Appendix A: Functions and Instructions
&
(append)
@ ¥ p
key
H
2
H key
string1 & string2
⇒
string
Returns a text string that is
string2
appended to
string1
.
"Hello " & "Nick"
¸
"Hello Nick"
‰
()
(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 ...
‰
()
can be nested to do multiple integrals. Integration
limits can depend on integration variables outside
them.
Note: See also
nInt()
.
‰
(
‰
(ln(x+y),y,0,x),x,0,a)
¸