Difference between revisions of "Integral Command"
From GeoGebra Manual
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:{{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>}} | :{{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> ] | ||
| − | :Gives the definite integral | + | :Gives the definite integral over the interval ''[a , b]'' with respect to the main variable. |
:{{note| 1=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 | + | :Gives the definite integral of the function over the interval ''[a , b]'' with respect to the main variable and shadows 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== | ||
;Integral[ <Function f> ] | ;Integral[ <Function f> ] | ||
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:{{example|1=<div><code><nowiki>Integral[cos(a t), t]</nowiki></code> yields <math>\frac{sin(a t)}{a} + c_1</math>.</div>}} | :{{example|1=<div><code><nowiki>Integral[cos(a t), t]</nowiki></code> yields <math>\frac{sin(a t)}{a} + c_1</math>.</div>}} | ||
;Integral[ <Function>, <Number a>, <Number b> ] | ;Integral[ <Function>, <Number a>, <Number b> ] | ||
| − | :Gives the definite integral | + | :Gives the definite integral over the interval ''[a , b]'' with respect to the main variable. |
:{{example|1=<div><code><nowiki>Integral[cos(x), a, b]</nowiki></code> yields <math>sin(b) - sin(a)</math>.</div>}} | :{{example|1=<div><code><nowiki>Integral[cos(x), a, b]</nowiki></code> yields <math>sin(b) - sin(a)</math>.</div>}} | ||
;Integral[ <Function f>, <Variable t>, <Number a>, <Number b> ] | ;Integral[ <Function f>, <Variable t>, <Number a>, <Number b> ] | ||
| − | :Gives the definite integral | + | :Gives the definite integral over the interval ''[a , b]'' with respect to the given variable. |
:{{example|1=<div><code><nowiki>Integral[cos(t), t, a, b]</nowiki></code> yields <math>sin(b) - sin(a)</math>.</div>}} | :{{example|1=<div><code><nowiki>Integral[cos(t), t, a, b]</nowiki></code> yields <math>sin(b) - sin(a)</math>.</div>}} | ||
Revision as of 11:08, 17 September 2012
- Integral[ <Function> ]
- Gives the indefinite integral with respect to the main variable.
- Example:
Integral[x^3]yields \frac{x^4}{4}.
- Integral[ <Function>, <Variable> ]
- Gives the partial integral 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 over the interval [a , b] with respect to the main variable.
- 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 over the interval [a , b] with respect to the main variable and shadows 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
- Integral[ <Function f> ]
- Gives the indefinite integral with respect to the main variable.
- Example:
Integral[cos(x)]yields sin(x) + c_1.
- Integral[ <Function f>, <Variable t> ]
- Gives the indefinite integral with respect to the given variable.
- Example:
Integral[cos(a t), t]yields \frac{sin(a t)}{a} + c_1.
- Integral[ <Function>, <Number a>, <Number b> ]
- Gives the definite integral over the interval [a , b] with respect to the main variable.
- Example:
Integral[cos(x), a, b]yields sin(b) - sin(a).
- Integral[ <Function f>, <Variable t>, <Number a>, <Number b> ]
- Gives the definite integral over the interval [a , b] with respect to the given variable.
- Example:
Integral[cos(t), t, a, b]yields sin(b) - sin(a).
