Difference between revisions of "Integral Command"
From GeoGebra Manual
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{{command|cas=true|function}} | {{command|cas=true|function}} | ||
;Integral[ <Function> ] | ;Integral[ <Function> ] | ||
− | :Gives the indefinite integral | + | :Gives the indefinite integral with respect to the main variable. |
:{{example|1=<div><code><nowiki>Integral[x^3]</nowiki></code> yields <math>\frac{x^4}{4}</math>.</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> ] | ||
− | :Gives the partial integral | + | :Gives the partial integral with respect to the given variable. |
:{{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, with respect to the main variable, in the interval ''[a , b]''. |
:{{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> ] | ||
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==CAS Syntax== | ==CAS Syntax== | ||
;Integral[ <Function f> ] | ;Integral[ <Function f> ] | ||
− | :Gives the indefinite integral | + | :Gives the indefinite integral with respect to the main variable. |
:{{example|1=<div><code><nowiki>Integral[cos(x)]</nowiki></code> yields <math>sin(x) + c_1</math>.</div>}} | :{{example|1=<div><code><nowiki>Integral[cos(x)]</nowiki></code> yields <math>sin(x) + c_1</math>.</div>}} | ||
;Integral[ <Function f>, <Variable t> ] | ;Integral[ <Function f>, <Variable t> ] | ||
− | : Gives the indefinite integral | + | : Gives the indefinite integral with respect to the given variable ''t''. |
:{{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, with respect to the main variable, in the interval ''[a , b]''. |
:{{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 in the interval ''[a , b] | + | :Gives the definite integral, with respect to the given variable, in the interval ''[a , b]''. |
:{{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 10:43, 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, 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 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 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, 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, with respect to the given variable, in the interval [a , b].
- Example:
Integral[cos(t), t, a, b]
yields sin(b) - sin(a).