# Difference between revisions of "IntegralBetween Command"

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;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 variable t. | ||

− | :{{example| 1=<div><code><nowiki>IntegralBetween[a * sin(t), a * cos(t), t, π / 4, π * 5 / 4]</nowiki></code> yields <math> | + | :{{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 10:30, 18 August 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*]. **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*] 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*]. **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 variable t. **Example:**`IntegralBetween[a * sin(t), a * cos(t), t, π / 4, π * 5 / 4]`

yields 2 \sqrt{2} a.