Do all continuous functions have antiderivatives? If not all continuous functions

Wade Bullock 2022-07-04 Answered
Do all continuous functions have antiderivatives?
If not all continuous functions are differentiable, so how is it that all continuous functions have anti-derivatives?
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Answers (1)

potamanixv
Answered 2022-07-05 Author has 15 answers
Step 1
Let I R be an interval with more than one point. If f : I R is a continuous function, the existence of an anti-derivative of f can be proved as follows: take a I and define
F : I R x a x f ( t ) d t .
Step 2
Then F is a primitive of f, by the Fundamental Theorem of Calculus.
You seem to find it strange that every continuous has an anti-derivative while not all continuous functions are differentiable, but it's up to you to explain what's strange about it.

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