908 Appendix A: Functions and Instructions
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) ¸
‡
‡‡
‡() (square root) 2]key
‡
‡‡
‡ (
expression1
) ⇒
⇒⇒
⇒
expression
‡
‡‡
‡ (
list1
) ⇒
⇒⇒
⇒
list
Returns the square root of the argument.
For a list, returns the square roots of all the
elements in
list1.
‡(4) ¸ 2
‡({9,a,4}) ¸ {3 ‡a 2}
Π() (product) MATH/Calculus menu
Π
ΠΠ
Π(
expression1
,
var
,
low
,
high
) ⇒
⇒⇒
⇒
expression
Evaluates
expression1
for each value of
var
from
low
to
high
, and returns the product of the results.
Π(1/n,n,1,5) ¸
1
120
Π(k^2,k,1,n) ¸ (n!)ñ
Π({1/n,n,2},n,1,5) ¸
{
1
120
120 32}
Π
ΠΠ
Π(
expression1
,
var
,
low
,
low
ì 1) ⇒
⇒⇒
⇒ 1
Π(k,k,4,3) ¸ 1
Π
ΠΠ
Π(
expression1
,
var
,
low
,
high
) ⇒
⇒⇒
⇒ 1
/
Π(
expression1,
var, high
+1,
low
ì 1)
if
high
<
low
ì 1
Π(1/k,k,4,1) ¸ 6
Π(1/k,k,4,1)ù Π(1/k,k,2,4) ¸
1/4
G() (sum) MATH/Calculus menu
G
GG
G (
expression1
,
var
,
low
,
high
) ⇒
⇒⇒
⇒
expression
Evaluates
expression1
for each value of
var
from
low
to
high
, and returns the sum of the results.
G(1/n,n,1,5) ¸
137
60
G(k^2,k,1,n) ¸
nø (n + 1)ø (2ø n + 1)
6
G(1/n^2,n,1,ˆ) ¸
pñ
6
G
GG
G (
expression1
,
var
,
low
,
low
ì 1) ⇒
⇒⇒
⇒ 0
G(k,k,4,3) ¸ 0
G
GG
G (
expression1
,
var
,
low
,
high
) ⇒
⇒⇒
⇒ ë G
GG
G (
expression1,
var, high
+1,
low
ì 1) if
high
<
low
ì 1
G(k,k,4,1) ¸ ë 5
G(k,k,4,1)+G(k,k,2,4) ¸ 4
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