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.
+
: Yields the indefinite integral for the given function with respect to the main variable.
 
:{{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> ]
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==CAS Syntax==
 
==CAS Syntax==
 
; Integral[ Function f]
 
; Integral[ Function f]
: Yields the indefinite integral for the given function.
+
: Yields 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>  returns sin(x)+c1.}}
 
; Integral[Function f, Variable t]
 
; Integral[Function f, Variable t]

Revision as of 10:37, 7 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 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 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 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]
Indefinite integral with respect to 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 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]
Definite integral from a to b with respect to variable t.
Example: Integral[cos(t), t, a, b] returns sin(b) - sin(a).
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