Difference between revisions of "Integral Command"

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:{{example|1=<div><code><nowiki>Integral[x³]</nowiki></code> yields ''  x⁴ / 4  ''.</div>}}
 
:{{example|1=<div><code><nowiki>Integral[x³]</nowiki></code> yields ''  x⁴ / 4  ''.</div>}}
 
;Integral[ <Function>, <Variable> ]
 
;Integral[ <Function>, <Variable> ]
:Returns the partial integral of the function with respect to the variable.
+
:Returns the partial integral of the function with respect to the given variable.
 
:{{example|1=<div><code><nowiki>Integral[x³+3x y, x]</nowiki></code> yields '' (x² (x² + 6y)) / 4 ''.</div>}}
 
:{{example|1=<div><code><nowiki>Integral[x³+3x y, x]</nowiki></code> yields '' (x² (x² + 6y)) / 4 ''.</div>}}
 
; Integral[Function, Number a, Number b]
 
; Integral[Function, Number a, Number b]
: Returns the definite integral of the function in the interval [''a , b''].
+
: Returns the definite integral of the function, with respect to the main variable, in the interval [''a , b''].
 
: {{Note| This command also shadows the area between the function graph of ''f'' and the ''x''-axis.}}
 
: {{Note| This command also shadows the area between the function graph of ''f'' and the ''x''-axis.}}
  
 
; Integral[Function, Number a, Number b, Boolean Evaluate]:  
 
; Integral[Function, Number a, Number b, Boolean Evaluate]:  
: Returns the definite integral of the function in the interval [''a , b''] and shadows the related area when ''Evaluate = true''.  In case ''Evaluate = false'' the related area is shaded but the integral value is not calculated.
+
: Returns the definite integral of the function, with respect to the main variable, in the interval [''a , b''] and shadows the related area when ''Evaluate = true''.  In case ''Evaluate = false'' the related area is shaded but the integral value is not calculated.
  
 
==CAS Syntax==
 
==CAS Syntax==
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:{{Example|1=<code><nowiki>Integral[cos(x)]</nowiki></code>  returns sin(x)+c1.}}
 
:{{Example|1=<code><nowiki>Integral[cos(x)]</nowiki></code>  returns sin(x)+c1.}}
 
; Integral[Function f, Variable t]
 
; Integral[Function f, Variable t]
: Indefinite integral with respect to variable ''t''.
+
: Returns the indefinite integral of the function with respect to the given variable ''t''.
 
:{{Example|1=<code><nowiki>Integral[cos(a t), t]</nowiki></code>  returns sin(a t)/a+c2.}}
 
:{{Example|1=<code><nowiki>Integral[cos(a t), t]</nowiki></code>  returns sin(a t)/a+c2.}}
 
; Integral[Function, Number a, Number b]
 
; Integral[Function, Number a, Number b]
: Returns the definite integral of the function in the interval [''a , b''].
+
: Returns the definite integral of the function, with respect to the main variable, in the interval [''a , b''].
 
:{{Example|1=<code><nowiki>Integral[cos(x), a, b]</nowiki></code>  returns sin(b) - sin(a).}}
 
:{{Example|1=<code><nowiki>Integral[cos(x), a, b]</nowiki></code>  returns sin(b) - sin(a).}}
 
; Integral[Function f, Variable t, Number a, Number b]
 
; Integral[Function f, Variable t, Number a, Number b]
: Definite integral from ''a'' to ''b'' with respect to variable ''t''.
+
: Returns the definite integral in the interval [''a , b''] with respect to the given variable ''t''.
 
:{{Example|1=<code><nowiki>Integral[cos(t), t, a, b]</nowiki></code>  returns sin(b) - sin(a).}}
 
:{{Example|1=<code><nowiki>Integral[cos(t), t, a, b]</nowiki></code>  returns sin(b) - sin(a).}}

Revision as of 13:33, 21 October 2011


Integral[Function]
Yields the indefinite integral for the given function with respect to the main variable.
Example:
Integral[x³] yields x⁴ / 4 .
Integral[ <Function>, <Variable> ]
Returns the partial integral of the function with respect to the given variable.
Example:
Integral[x³+3x y, x] yields (x² (x² + 6y)) / 4 .
Integral[Function, Number a, Number b]
Returns the definite integral of the function, with respect to the main variable, in the interval [a , b].
Note: This command also shadows the area between the function graph of f and the x-axis.
Integral[Function, Number a, Number b, Boolean Evaluate]
Returns the definite integral of the function, with respect to the main variable, in the interval [a , b] and shadows the related area when Evaluate = true. In case Evaluate = false the related area is shaded but the integral value is not calculated.

CAS Syntax

Integral[ Function f]
Yields the indefinite integral for the given function with respect to the main variable.
Example: Integral[cos(x)] returns sin(x)+c1.
Integral[Function f, Variable t]
Returns the indefinite integral of the function with respect to the given variable t.
Example: Integral[cos(a t), t] returns sin(a t)/a+c2.
Integral[Function, Number a, Number b]
Returns the definite integral of the function, with respect to the main variable, in the interval [a , b].
Example: Integral[cos(x), a, b] returns sin(b) - sin(a).
Integral[Function f, Variable t, Number a, Number b]
Returns the definite integral in the interval [a , b] with respect to the given variable t.
Example: Integral[cos(t), t, a, b] returns sin(b) - sin(a).
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