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> ] |
| − | : | + | :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''.}} | + | :{{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 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> ] |
| − | : | + | :Gives the definite integral of the difference ''f(x) ‐ g(x)'' over 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> | + | :{{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> ] |
| − | : | + | :Gives the definite integral of the difference ''f(x) ‐ g(x)'' over the interval ''[a, b]'' with respect to the given variable. |
| − | :{{example| 1=<div><code><nowiki>IntegralBetween[a * sin(t), a * cos(t), t, π / 4, π * 5 / 4]</nowiki></code> | + | :{{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 11:00, 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 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> ]
- 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.
