Texas Instruments TITANIUM TI-89 - Manual (Page 907)

Appendix A: Functions and Instructions 907
& (append) ¥ p 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) ¸
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
‰ (aù x^2,x,c) ¸
aø xò
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/(2ì cos(x)),x)! tmp(x) ¸
ClrGraph:Graph tmp(x):Graph
1/(2ì cos(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.
‰ (bù 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) ¸