Difference between revisions of "IntegralBetween Command"

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:{{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> ]
 
;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 if ''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 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> ]
 
;IntegralBetween[ <Function f>, <Function g>, <Number a>, <Number b> ]

Revision as of 11:05, 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 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 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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