Difference between revisions of "IntegralBetween Command"

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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
 
<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
 
{{command|cas=true|function}}
 
{{command|cas=true|function}}
;IntegralBetween[Function f, Function g, Number a, Number b]
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;IntegralBetween[ >Function f>, <Function g>, <Number a>, <Number b> ]
:Returns the definite integral of the difference ''f(x) ‐ g(x)'' in the interval [''a, b''] with respect to the main variable.
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:Gives the definite integral of the difference ''f(x) ‐ g(x)'' over the interval ''[a, b]'' with respect to the main variable.
:{{note| This command also shades the area between the function graphs of ''f'' and ''g''.}}
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:{{note| 1=This command also shades the area between the function graphs of ''f'' and ''g''.}}
;IntegralBetween[Function f, Function g, Number a, Number b, Boolean Evaluate]
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;IntegralBetween[ <Function f>, <Function g>, <Number a>, <Number b>, <Boolean Evaluate> ]
:Returns the definite integral of the difference ''f(x) ‐ g(x)'' in the interval [''a, b''] with respect to the main variable and shadows the related area when ''Evaluate = true''.  In case ''Evaluate = false'' the related area is shaded but the integral value is not calculated.
+
:Gives the definite integral of the difference ''f(x) ‐ g(x)'' over the interval ''[a, b]'' with respect to the main variable 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==
;IntegralBetween[ Function f, Function g, Number a, Number b]
+
;IntegralBetween[ <Function f>, <Function g>, <Number a>, <Number b> ]
:Returns the definite integral of the difference ''f(x) ‐ g(x)'' in the interval [''a, b''] with respect to the main variable.
+
:Gives the definite integral of the difference ''f(x) ‐ g(x)'' over the interval ''[a, b]'' with respect to the main variable.
:{{example| 1=<div><code><nowiki>IntegralBetween[sin(x), cos(x), π / 4, π * 5 / 4]</nowiki></code> yields <math>2 \sqrt{2}</math>.</div>}}
+
:{{example| 1=<div><code><nowiki>IntegralBetween[sin(x), cos(x), π / 4, π * 5 / 4]</nowiki></code> yields <math>2 \sqrt{2}</math>.</div>}}
;IntegralBetween[ Function f, Function g, Variable t, Number a, Number b ]
+
;IntegralBetween[ <Function f>, <Function g>, <Variable t>, <Number a>, <Number b> ]
:Returns the definite integral of the difference ''f ‐ g'' in the interval [''a, b''] with respect to the given variable t.
+
:Gives the definite integral of the difference ''f(x) ‐ g(x)'' over the interval ''[a, b]'' with respect to the given variable.
:{{example| 1=<div><code><nowiki>IntegralBetween[a * sin(t), a * cos(t), t, π / 4, π * 5 / 4]</nowiki></code> yields <math>2 \sqrt{2} a</math>.</div>}}
+
:{{example| 1=<div><code><nowiki>IntegralBetween[a * sin(t), a * cos(t), t, π / 4, π * 5 / 4]</nowiki></code> yields <math>2 \sqrt{2} a</math>.</div>}}

Revision as of 11:00, 17 September 2012


IntegralBetween[ >Function f>, <Function g>, <Number a>, <Number b> ]
Gives the definite integral of the difference f(x) ‐ g(x) over the interval [a, b] with respect to the main variable.
Note: This command also shades the area between the function graphs of f and g.
IntegralBetween[ <Function f>, <Function g>, <Number a>, <Number b>, <Boolean Evaluate> ]
Gives the definite integral of the difference f(x) ‐ g(x) over the interval [a, b] with respect to the main variable 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

IntegralBetween[ <Function f>, <Function g>, <Number a>, <Number b> ]
Gives the definite integral of the difference f(x) ‐ g(x) over the interval [a, b] with respect to the main variable.
Example:
IntegralBetween[sin(x), cos(x), π / 4, π * 5 / 4] yields 2 \sqrt{2}.
IntegralBetween[ <Function f>, <Function g>, <Variable t>, <Number a>, <Number b> ]
Gives the definite integral of the difference f(x) ‐ g(x) over the interval [a, b] with respect to the given variable.
Example:
IntegralBetween[a * sin(t), a * cos(t), t, π / 4, π * 5 / 4] yields 2 \sqrt{2} a.
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