Difference between revisions of "IntegralBetween Command"

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;IntegralBetween[ >Function f>, <Function g>, <Number a>, <Number b> ]
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;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.
 
:Gives the definite integral of the difference ''f(x) ‐ g(x)'' over the interval ''[a, b]'' with respect to the main variable.
 
:{{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''.}}

Revision as of 10:10, 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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