DeltaFunction[x]
is the Dirac delta-function \delta (x).
Mathematica also provides a built-in function DiracDelta
with comparable properties.
Overview, Convolute, DeltaFunctionPrime, Integrate2, SimplifyDeltaFunction.
[1 - x] DeltaFunction
\delta (1-x)
[DeltaFunction[1 - x] f[x], {x, 0, 1}] Integrate2
f(1)
[DeltaFunction[x] f[x], {x, 0, 1}] Integrate2
f(0)
[DeltaFunction[1 - x] f[x], {x, 0, 1}] Integrate2
f(1)
[DeltaFunction[1 - x], x] /. FCGV[z_] :> ToExpression[z] Convolute
-x \delta (1-x) \log (x)