Difference between revisions of "Integral Command"

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(* in some versions of GeoGebra, a numerical algorithm is used so integrating up to an asypmtote or similar eg <code>Integral(ln(x), 0, 1)</code> won't work. In this case try <code>Integral(ln(x), 0, 1, false)</code>)
 
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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}}
==Definite integral==
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;Integral( <Function> )
; Integral[Function, Number a, Number b]: Returns the definite integral of the function in the interval [''a , b''].
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:Gives the indefinite integral with respect to the main variable.
: {{Note| This command also draws the area between the function graph of ''f'' and the ''x''-axis.}}
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:{{example|1=<code><nowiki>Integral(x^3)</nowiki></code> yields <math>x^4 \cdot 0.25</math>.}}
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;Integral( <Function>, <Variable> )
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:Gives the partial integral with respect to the given variable.
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:{{Example|1=<code><nowiki>Integral(x³+3x y, x)</nowiki></code>  gives'' <math>\frac{1}{4}x^4</math> + <math>\frac{3}{2}</math> x² y '' .}}
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;Integral( <Function>, <Start x-Value>, <End x-Value> )
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:Gives the definite integral over the interval ''[Start x-Value , End x-Value]'' with respect to the main variable.
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:{{note| 1=This command also shades the area between the function graph of ''f'' and the ''x''-axis.}}
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;Integral( <Function>, <Start x-Value>, <End x-Value>, <Boolean Evaluate> )
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:Gives the definite integral of the function over the interval ''[Start x-Value , End x-Value]'' with respect to the main variable and shades the related area if ''Evaluate'' is ''true''.  In case ''Evaluate'' is ''false'' the related area is shaded but the integral value is not calculated.
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==CAS Syntax==
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In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] undefined variables are allowed as input as well.
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:{{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, Boolean Evaluate]: {{description}}
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Furthermore, the following command is only available in the [[File:Menu view cas.svg|link=|16px]] ''CAS View'':
  
; Integral[Function f, Function g, Number a, Number b]: Yields the definite integral of the difference ''f(x) ‐ g(x)'' in the interval [''a, b''].
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;Integral( <Function>, <Variable>, <Start x-Value>, <End x-Value> )
: {{Note| This command also draws the area between the function graphs of ''f'' and ''g''.}}
+
:Gives the definite integral over the interval ''[Start x-Value , End x-Value]'' with respect to the given variable.
 +
:{{example|1=<code><nowiki>Integral(cos(t), t, a, b)</nowiki></code> yields <math>- sin(a) + sin(b)</math>.}}
  
; Integral[Function f, Function g, Number a, Number b, Boolean Evaluate]: {{description}}
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{{note| 1=<div>
==Indefinite integral==
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* The answer isn't guaranteed to be continuous, eg <code>Integral(floor(x))</code>, that is the integral of the function ⌊x⌋  - in that case you can define your own function to use eg <code>F(x)=(floor(x)² - floor(x))/2 + x floor(x) - floor(x)²</code>, i.e. the function <math>\frac{⌊x⌋² - ⌊x⌋}{2} + x \cdot⌊x⌋ - ⌊x⌋²</math>
;Integral[Function]: Yields the indefinite integral for the given function.
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* in some versions of GeoGebra, a numerical algorithm is used so integrating up to an asypmtote or similar eg <code>Integral(ln(x), 0, 1)</code> won't work. In this case try <code>Integral(ln(x), 0, 1, false)</code>
 +
</div>}}

Latest revision as of 12:11, 20 March 2019


Integral( <Function> )
Gives the indefinite integral with respect to the main variable.
Example: Integral(x^3) yields x^4 \cdot 0.25.
Integral( <Function>, <Variable> )
Gives the partial integral with respect to the given variable.
Example: Integral(x³+3x y, x) gives \frac{1}{4}x^4 + \frac{3}{2} x² y .
Integral( <Function>, <Start x-Value>, <End x-Value> )
Gives the definite integral over the interval [Start x-Value , End x-Value] with respect to the main variable.
Note: This command also shades the area between the function graph of f and the x-axis.
Integral( <Function>, <Start x-Value>, <End x-Value>, <Boolean Evaluate> )
Gives the definite integral of the function over the interval [Start x-Value , End x-Value] with respect to the main variable and shades the related area if Evaluate is true. In case Evaluate is false the related area is shaded but the integral value is not calculated.

CAS Syntax

In the Menu view cas.svg CAS View undefined variables are allowed as input as well.

Example: Integral(cos(a t), t) yields \frac{sin(a t)}{a} + c_1.


Furthermore, the following command is only available in the Menu view cas.svg CAS View:

Integral( <Function>, <Variable>, <Start x-Value>, <End x-Value> )
Gives the definite integral over the interval [Start x-Value , End x-Value] with respect to the given variable.
Example: Integral(cos(t), t, a, b) yields - sin(a) + sin(b).


Note:
  • The answer isn't guaranteed to be continuous, eg Integral(floor(x)), that is the integral of the function ⌊x⌋ - in that case you can define your own function to use eg F(x)=(floor(x)² - floor(x))/2 + x floor(x) - floor(x)², i.e. the function \frac{⌊x⌋² - ⌊x⌋}{2} + x \cdot⌊x⌋ - ⌊x⌋²
  • in some versions of GeoGebra, a numerical algorithm is used so integrating up to an asypmtote or similar eg Integral(ln(x), 0, 1) won't work. In this case try Integral(ln(x), 0, 1, false)
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