Difference between revisions of "IntegralBetween Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}}
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;IntegralBetween( <Function>, <Function>, <Number>, <Number> )
;IntegralBetween[ <Function f>, <Function g>, <Number a>, <Number b> ]
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:Gives the definite integral of the difference ''f(x) ‐ g(x)'' of two function ''f'' and ''g'' over the interval ''[a, b]'', where ''a'' is the first number and ''b'' the second, 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.
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:{{example| 1=<code><nowiki>IntegralBetween(sin(x), cos(x), 0, pi)</nowiki></code>}}
 
:{{note| 1=This command also shades the area between the function graphs of ''f'' and ''g''.}}
 
:{{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>, <Function>, <Number>, <Number>, <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 if ''Evaluate'' is ''true''.  In case ''Evaluate'' is ''false'' the related area is shaded but the integral value is not calculated.
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:Gives the definite integral of the difference ''f(x) ‐ g(x)'' of two function ''f'' and ''g'' over the interval ''[a, b]'', where ''a'' is the first number and ''b'' the second, 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==
;IntegralBetween[ <Function f>, <Function g>, <Number a>, <Number b> ]
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;IntegralBetween( <Function>, <Function>, <Number>, <Number> )
:Gives the definite integral of the difference ''f(x) ‐ g(x)'' over the interval ''[a, b]'' with respect to the main variable.
+
:Gives the definite integral of the difference ''f(x) ‐ g(x)'' of two function ''f'' and ''g'' over the interval ''[a, b]'', where ''a'' is the first number and ''b'' the second, 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>}}
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:{{example| 1=<code><nowiki>IntegralBetween(sin(x), cos(x), pi / 4, pi * 5 / 4)</nowiki></code> yields <math>2 \sqrt{2}</math>.}}
;IntegralBetween[ <Function f>, <Function g>, <Variable t>, <Number a>, <Number b> ]
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;IntegralBetween( <Function>, <Function>, <Variable>, <Number>, <Number> )
:Gives the definite integral of the difference ''f(x) ‐ g(x)'' over the interval ''[a, b]'' with respect to the given variable.
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:Gives the definite integral of a variable of the difference ''f(x) ‐ g(x)'' of two function ''f'' and ''g'' over the interval ''[a, b]'', where ''a'' is the first number and ''b'' the second, 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>}}
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:{{example| 1=<code><nowiki>IntegralBetween(a * sin(t), a * cos(t), t, pi / 4, pi * 5 / 4)</nowiki></code> yields <math>2 \sqrt{2} a</math>.}}

Latest revision as of 08:27, 9 October 2017


IntegralBetween( <Function>, <Function>, <Number>, <Number> )
Gives the definite integral of the difference f(x) ‐ g(x) of two function f and g over the interval [a, b], where a is the first number and b the second, with respect to the main variable.
Example: IntegralBetween(sin(x), cos(x), 0, pi)
Note: This command also shades the area between the function graphs of f and g.
IntegralBetween( <Function>, <Function>, <Number>, <Number>, <Boolean Evaluate> )
Gives the definite integral of the difference f(x) ‐ g(x) of two function f and g over the interval [a, b], where a is the first number and b the second, 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

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