Function that has no antiderivativeCan someone give an example of a function f : ] − 1 , 1 [ → R that has no antiderivative? Is there a certain "class" of functions which share this characteristic? Thank you in advance.

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Function that has no antiderivativeCan someone give an example of a function   f  :   ]  −  1  ,  1  [  →      R   that has no antiderivative? Is there a certain &quot;class&quot; of functions which share this characteristic? Thank you in advance.

Savanah Hernandez · Accepted Answer

Explanation:As the previous answer suggests, the good example is the signum function. If       F    ′    (  x  )  =  sgn  ⁡  (  x  ) for any x, then       F    ′    (  x  )  =  1 if   x  &amp;gt;  0, so then   F  (  x  )  =  x  +  C. Similarly for   x  &amp;lt;  0 we have   F  (  x  )  =  −  x  +  D. Of course, F should be continuous at 0. Because   F  (  0  +  )  =  C and   F  (  0  −  )  =  D, we get   F  (  0  )  =  C  =  D. Hence   F  (  x  )  =      |    x      |    +  C for any x. But F is not differentiable and it could not be an antiderivative.

Function that has no antiderivative Can someone give an example of a function f : ]

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