# Difference between revisions of "IntegralBetween Command"

From GeoGebra Manual

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | ||

− | ;IntegralBetween | + | ;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. | :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), 0, pi]</nowiki></code></div>}} | :{{example| 1=<div><code><nowiki>IntegralBetween[sin(x), cos(x), 0, pi]</nowiki></code></div>}} | ||

:{{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 | + | ;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. | :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 | + | ;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| 1=<div><code><nowiki>IntegralBetween[sin(x), cos(x), pi / 4, pi * 5 / 4]</nowiki></code> yields <math>2 \sqrt{2}</math>.</div>}} | :{{example| 1=<div><code><nowiki>IntegralBetween[sin(x), cos(x), pi / 4, pi * 5 / 4]</nowiki></code> yields <math>2 \sqrt{2}</math>.</div>}} | ||

− | ;IntegralBetween | + | ;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. | :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, pi / 4, pi * 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, pi / 4, pi * 5 / 4]</nowiki></code> yields <math>2 \sqrt{2} a</math>.</div>}} |

## Revision as of 17:17, 7 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.