Difference between revisions of "IntegralBetween Command"

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{{command|cas=true|function}}
 
{{command|cas=true|function}}
 
;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''].
+
:Returns the definite integral of the difference ''f(x) ‐ g(x)'' in 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''.}}
 
:{{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]
 
;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''] 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 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.
 
==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''].
+
:Returns the definite integral of the difference ''f(x) ‐ g(x)'' in 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 variable t.
+
:Returns the definite integral of the difference ''f ‐ g'' in the interval [''a, b''] with respect to the given variable t.
 
:{{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 13:40, 21 October 2011


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.
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]
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.

CAS Syntax

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.
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 ]
Returns the definite integral of the difference f ‐ g in the interval [a, b] with respect to the given variable t.
Example:
IntegralBetween[a * sin(t), a * cos(t), t, π / 4, π * 5 / 4] yields 2 \sqrt{2} a.
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