Difference between revisions of "Integral Command"
From GeoGebra Manual
m (changed CAS syntax description) |
m (Text replace - ";(.*)\[(.*)\]" to ";$1($2)") |
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | ||
| − | ;Integral | + | ;Integral( <Function> ) |
:Gives the indefinite integral with respect to the main variable. | :Gives the indefinite integral with respect to the main variable. | ||
:{{example|1=<div><code><nowiki>Integral[x^3]</nowiki></code> yields <math>x^4 \cdot 0.25</math>.</div>}} | :{{example|1=<div><code><nowiki>Integral[x^3]</nowiki></code> yields <math>x^4 \cdot 0.25</math>.</div>}} | ||
| − | ;Integral | + | ;Integral( <Function>, <Variable> ) |
:Gives the partial integral with respect to the given variable. | :Gives the partial integral with respect to the given variable. | ||
:{{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 '' .}} | :{{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 '' .}} | ||
| − | ;Integral | + | ;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. | :Gives the definite integral over the interval ''[Start x-Value , End x-Value]'' with respect to the main variable. | ||
:{{note| 1=This command also shades the area between the function graph of ''f'' and the ''x''-axis.}} | :{{note| 1=This command also shades the area between the function graph of ''f'' and the ''x''-axis.}} | ||
| − | ;Integral | + | ;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. | :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== | ==CAS Syntax== | ||
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Furthermore, the following command is only available in the [[File:Menu view cas.svg|link=|16px]] ''CAS View'': | Furthermore, the following command is only available in the [[File:Menu view cas.svg|link=|16px]] ''CAS View'': | ||
| − | ;Integral | + | ;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. | :Gives the definite integral over the interval ''[Start x-Value , End x-Value]'' with respect to the given variable. | ||
:{{example|1=<div><code><nowiki>Integral[cos(t), t, a, b]</nowiki></code> yields <math>- sin(a) + sin(b)</math>.</div>}} | :{{example|1=<div><code><nowiki>Integral[cos(t), t, a, b]</nowiki></code> yields <math>- sin(a) + sin(b)</math>.</div>}} | ||
Revision as of 17:16, 7 October 2017
- 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 
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 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).
