Difference between revisions of "Integral Command"

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{{command|cas=true|function}}
 
{{command|cas=true|function}}
 
;Integral[ <Function> ]
 
;Integral[ <Function> ]
: Yields the indefinite integral for the given function with respect to the main variable.
+
:Gives the indefinite integral for the given function with respect to the main variable.
:{{example|1=<div><code><nowiki>Integral[]</nowiki></code> yields ''  x⁴ / 4  ''.</div>}}
+
:{{example|1=<div><code><nowiki>Integral[x^3]</nowiki></code> yields <math>\frac{x^4}{4}</math>.</div>}}
 
;Integral[ <Function>, <Variable> ]
 
;Integral[ <Function>, <Variable> ]
:Returns the partial integral of the function with respect to the given variable.
+
:Gives the partial integral of the function with respect to the given variable.
:{{example|1=<div><code><nowiki>Integral[+3x y, x]</nowiki></code> yields '' (x² (x² + 6y)) / 4 ''.</div>}}
+
:{{example|1=<div><code><nowiki>Integral[x^3 + 3 x y, x]</nowiki></code> yields <math>\frac{x^4 + 6 x^2 y}{4}</math>.</div>}}
; Integral[ <Function>, <Number a>, <Number b> ]
+
;Integral[ <Function>, <Number a>, <Number b> ]
: Returns the definite integral of the function, with respect to the main variable, in the interval [''a , b''].
+
:Gives 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| 1=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> ]:
+
:Gives the definite integral of the function, with respect to the main variable, in the interval ''[a , b]'' and shadows the related area ''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==
; Integral[ Function f]
+
;Integral[ <Function f> ]
: Yields the indefinite integral for the given function with respect to the main variable.
+
:Gives the indefinite integral for the given function with respect to the main variable.
:{{Example|1=<code><nowiki>Integral[cos(x)]</nowiki></code> returns sin(x)+c1.}}
+
:{{example|1=<code><nowiki>Integral[cos(x)]</nowiki></code> yields <math>sin(x) + c_1</math>.}}
; Integral[ <Function f>, <Variable t> ]
+
;Integral[ <Function f>, <Variable t> ]
: Returns the indefinite integral of the function with respect to the given variable ''t''.
+
: Gives 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> yields <math>\frac{sin(a t)}{a} + c_1</math>.}}
; Integral[ <Function>, <Number a>, <Number b> ]
+
;Integral[ <Function>, <Number a>, <Number b> ]
: Returns the definite integral of the function, with respect to the main variable, in the interval [''a , b''].
+
:Gives 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> yields <math>sin(b) - sin(a)</math>.}}
; Integral[ <Function f>, <Variable t>, <Number a>, <Number b> ]
+
;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''.
+
:Gives 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> yields <math>sin(b) - sin(a)</math>.}}

Revision as of 09:36, 17 September 2012


Integral[ <Function> ]
Gives the indefinite integral for the given function with respect to the main variable.
Example:
Integral[x^3] yields \frac{x^4}{4}.
Integral[ <Function>, <Variable> ]
Gives the partial integral of the function with respect to the given variable.
Example:
Integral[x^3 + 3 x y, x] yields \frac{x^4 + 6 x^2 y}{4}.
Integral[ <Function>, <Number a>, <Number b> ]
Gives 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> ]
Gives the definite integral of the function, with respect to the main variable, in the interval [a , b] and shadows the related area Evaluate = true. In case Evaluate = false the related area is shaded but the integral value is not calculated.

CAS Syntax

Integral[ <Function f> ]
Gives the indefinite integral for the given function with respect to the main variable.
Example: Integral[cos(x)] yields sin(x) + c_1.
Integral[ <Function f>, <Variable t> ]
Gives the indefinite integral of the function with respect to the given variable t.
Example: Integral[cos(a t), t] yields \frac{sin(a t)}{a} + c_1.
Integral[ <Function>, <Number a>, <Number b> ]
Gives the definite integral of the function, with respect to the main variable, in the interval [a , b].
Example: Integral[cos(x), a, b] yields sin(b) - sin(a).
Integral[ <Function f>, <Variable t>, <Number a>, <Number b> ]
Gives the definite integral in the interval [a , b] with respect to the given variable t.
Example: Integral[cos(t), t, a, b] yields sin(b) - sin(a).
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