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)
¸
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) ¸
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