Difference between revisions of "IntegralBetween Command"
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;IntegralBetween[Function f, Function g, Number a, Number b] | ;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'']. | + | :Returns the definite integral of the difference ''f(x) ‐ g(x)'' in 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| 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] | ||
| − | :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. | + | :Returns the definite integral of the difference ''f(x) ‐ g(x)'' in 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] | ||
| − | :Returns the definite integral of the difference ''f(x) ‐ g(x)'' in the interval [''a, b'']. | + | :Returns the definite integral of the difference ''f(x) ‐ g(x)'' in 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> yields <math>2 \sqrt{2}</math>.</div>}} | :{{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 ] | ||
| − | :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 given variable t. |
:{{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>}} | :{{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 13:40, 21 October 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] 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]
- Returns the definite integral of the difference f(x) ‐ g(x) in 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]
- Returns the definite integral of the difference f(x) ‐ g(x) in 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 ]
- Returns the definite integral of the difference f ‐ g in the interval [a, b] with respect to the given variable t.
- Example:
IntegralBetween[a * sin(t), a * cos(t), t, π / 4, π * 5 / 4]yields 2 \sqrt{2} a.
