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I am a bit confused, why Mathematica can not solve this task:

Integrate[HeavisideTheta[x] f''[x], {x, 0, xf}, Assumptions -> {∞ > xf > 0}]

Do I need some additional Assumptions for the Heaviside function? I would expect a solution like:

f'[xf]-f'[0]
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1 Answer 1

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You need to help out Limit here. The option Analytic needs to be set to True.

SetOptions[Limit, Analytic -> True];
Integrate[HeavisideTheta[x] f''[x], {x, 0, xf}, Assumptions -> 0 < xf < ∞]
(* -Derivative[1][f][0] + Derivative[1][f][xf] *)
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