Providing additional information for Mathematica to simplify expressions
Sometimes we know that some variables are positive or natural numbers or real, and this helps to simplify expressions. For example,
Integrate[Sign[x], {x, -l/2, l}]
assessed as
ConditionalExpression[
1/2 l (-3 + 6 DiscreteDelta[l] + 2 HeavisideTheta[-l] +
4 HeavisideTheta[l]), l \[Element] Reals]
But if I know that l is a real positive number, I actually look at -l / 2. Is there a way to specify this additional information or limitation so that Mathematica can simplify the expression?
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2 answers
It will usually evaluate faster if you include Assumptions
inside Integrate
:
Integrate[Sign[x], {x, -l/2, l}, Assumptions -> l > 0]
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