Difference between revisions of "Integral Command"
From GeoGebra Manual
| Line 5: | Line 5: | ||
:{{example|1=<div><code><nowiki>Integral[x³]</nowiki></code> yields '' x⁴ / 4 ''.</div>}} | :{{example|1=<div><code><nowiki>Integral[x³]</nowiki></code> yields '' x⁴ / 4 ''.</div>}} | ||
;Integral[ <Function>, <Variable> ] | ;Integral[ <Function>, <Variable> ] | ||
| − | :Returns the partial integral of the function with respect to the variable. | + | :Returns the partial integral of the function with respect to the given variable. |
:{{example|1=<div><code><nowiki>Integral[x³+3x y, x]</nowiki></code> yields '' (x² (x² + 6y)) / 4 ''.</div>}} | :{{example|1=<div><code><nowiki>Integral[x³+3x y, x]</nowiki></code> yields '' (x² (x² + 6y)) / 4 ''.</div>}} | ||
; Integral[Function, Number a, Number b] | ; Integral[Function, Number a, Number b] | ||
| − | : Returns the definite integral of the function in the interval [''a , b'']. | + | : Returns the definite integral of the function, 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.}} | : {{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]: | ; Integral[Function, Number a, Number b, Boolean Evaluate]: | ||
| − | : Returns the definite integral of the function in the interval [''a , b''] and shadows the related area when ''Evaluate = true''. In case ''Evaluate = false'' the related area is shaded but the integral value is not calculated. | + | : Returns the definite integral of the function, with respect to the main variable, in the interval [''a , b''] and shadows the related area when ''Evaluate = true''. In case ''Evaluate = false'' the related area is shaded but the integral value is not calculated. |
==CAS Syntax== | ==CAS Syntax== | ||
| Line 19: | Line 19: | ||
:{{Example|1=<code><nowiki>Integral[cos(x)]</nowiki></code> returns sin(x)+c1.}} | :{{Example|1=<code><nowiki>Integral[cos(x)]</nowiki></code> returns sin(x)+c1.}} | ||
; Integral[Function f, Variable t] | ; Integral[Function f, Variable t] | ||
| − | : | + | : Returns the indefinite integral of the function with respect to the given variable ''t''. |
:{{Example|1=<code><nowiki>Integral[cos(a t), t]</nowiki></code> returns sin(a t)/a+c2.}} | :{{Example|1=<code><nowiki>Integral[cos(a t), t]</nowiki></code> returns sin(a t)/a+c2.}} | ||
; Integral[Function, Number a, Number b] | ; Integral[Function, Number a, Number b] | ||
| − | : Returns the definite integral of the function in the interval [''a , b'']. | + | : Returns the definite integral of the function, with respect to the main variable, in the interval [''a , b'']. |
:{{Example|1=<code><nowiki>Integral[cos(x), a, b]</nowiki></code> returns sin(b) - sin(a).}} | :{{Example|1=<code><nowiki>Integral[cos(x), a, b]</nowiki></code> returns sin(b) - sin(a).}} | ||
; Integral[Function f, Variable t, Number a, Number b] | ; Integral[Function f, Variable t, Number a, Number b] | ||
| − | : | + | : Returns the definite integral in the interval [''a , b''] with respect to the given variable ''t''. |
:{{Example|1=<code><nowiki>Integral[cos(t), t, a, b]</nowiki></code> returns sin(b) - sin(a).}} | :{{Example|1=<code><nowiki>Integral[cos(t), t, a, b]</nowiki></code> returns sin(b) - sin(a).}} | ||
Revision as of 13:33, 21 October 2011
- Integral[Function]
- Yields the indefinite integral for the given function with respect to the main variable.
- Example:
Integral[x³]yields x⁴ / 4 .
- Integral[ <Function>, <Variable> ]
- Returns the partial integral of the function with respect to the given variable.
- Example:
Integral[x³+3x y, x]yields (x² (x² + 6y)) / 4 .
- Integral[Function, Number a, Number b]
- Returns the definite integral of the function, 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]
- Returns the definite integral of the function, with respect to the main variable, in the interval [a , b] and shadows the related area when Evaluate = true. In case Evaluate = false the related area is shaded but the integral value is not calculated.
CAS Syntax
- Integral[ Function f]
- Yields the indefinite integral for the given function with respect to the main variable.
- Example:
Integral[cos(x)]returns sin(x)+c1.
- Integral[Function f, Variable t]
- Returns the indefinite integral of the function with respect to the given variable t.
- Example:
Integral[cos(a t), t]returns sin(a t)/a+c2.
- Integral[Function, Number a, Number b]
- Returns the definite integral of the function, with respect to the main variable, in the interval [a , b].
- Example:
Integral[cos(x), a, b]returns sin(b) - sin(a).
- Integral[Function f, Variable t, Number a, Number b]
- Returns the definite integral in the interval [a , b] with respect to the given variable t.
- Example:
Integral[cos(t), t, a, b]returns sin(b) - sin(a).
