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, with respect to the main variable, | + | :Gives the definite integral, with respect to the main variable, over 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> ] | ||
| − | :Gives the definite integral of the function, with respect to the main variable, | + | :Gives the definite integral of the function, with respect to the main variable, over 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== | ==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, with respect to the main variable, | + | :Gives the definite integral, with respect to the main variable, over 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, with respect to the given variable, | + | :Gives the definite integral, with respect to the given variable, over 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 10:46, 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, over 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, over 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.
- 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, over 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, over the interval [a , b].
- Example:
Integral[cos(t), t, a, b]yields sin(b) - sin(a).
