INT FROM ... TO: Difference between revisions
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Create an integral from the lower bound to the upper bound. The integral can then be symbolically evaluated with the [[SIMPLIFY|simplification]] type <code>integrate</code>. | Create an integral from the lower bound to the upper bound. The integral can then be symbolically evaluated with the [[SIMPLIFY|simplification]] type <code>integrate</code>. | ||
The [[differential]] can be contained in the expression and iMath will find it (you might have to expand the expression first). But if there is no [[differential]] matching the integration variable anywhere, then you will get strange results from the evaluation. | |||
The integrand must be enclosed in curly brackets. If the upper bound is a number or a variable then the curly braces around it can be omitted. | |||
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<code>@int@ EQDEF z = INT FROM x = -%pi to %pi { sin(x) differential(x)}</code> defines the integral and <code>@simp@ EQDEF SIMPLIFY(@int@, "integrate")<code> will evaluate it to the value 0. | <code>@int@ EQDEF z = INT FROM x = -%pi to %pi { sin(x) differential(x)}</code> defines the integral and <code>@simp@ EQDEF SIMPLIFY(@int@, "integrate")</code> will evaluate it to the value 0. | ||
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[[INT]] [[INTEGRATE]] | |||
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[[Category:Definition]] | [[Category:Definition]] | ||
Latest revision as of 19:21, 27 June 2017
Syntax
INT FROM symbol = expression TO { expression} { expression differential(symbol)}
Implemented in iMath since version 2.2.0 or earlier.
Explanation
Create an integral from the lower bound to the upper bound. The integral can then be symbolically evaluated with the simplification type integrate.
The differential can be contained in the expression and iMath will find it (you might have to expand the expression first). But if there is no differential matching the integration variable anywhere, then you will get strange results from the evaluation.
The integrand must be enclosed in curly brackets. If the upper bound is a number or a variable then the curly braces around it can be omitted.
Example
@int@ EQDEF z = INT FROM x = -%pi to %pi { sin(x) differential(x)} defines the integral and @simp@ EQDEF SIMPLIFY(@int@, "integrate") will evaluate it to the value 0.