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wolfram-mathematicaconstraintssymbolic-math

Specifying extra information to Mathematica for Simplifying expressions

Sometimes, we know that certain variables are positive, or natural numbers, or real and it helps to simplify the expressions. For example,

Integrate[Sign[x], {x, -l/2, l}]

evaluates to 

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 am actually looking at -l/2. Is there a way to specify this extra information or constraint so Mathematica can simplify the expression?

Solution

  • It will usually evaluate faster if you specify Assumptions inside of Integrate:

    Integrate[Sign[x], {x, -l/2, l}, Assumptions -> l > 0]