Recently we learned the fundamental theorem of calculus and subsequently Leibniz-Newton formula, that linked the primitive with the definite integral. I know that Leibniz-Newton can be applied when the funcition is both integrable and primitivable, but not necessarily continuous. This led to the drawing below. Although I can easily find examples of functions that are only integrable and not primitivable and in the comments there is allready a function that is only primitivable and not integrable, i cannot seem to find a function that is both integrable and primitivable but not continuous.
- Could you find such a function?
Here is a depiction of the inclusion I've been shown in class.
