Is there a general formula for antiderivatives the same way there is for derivatives?So, I know that first-order derivatives can be calculated with the formula: f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h Is there such a limit/standard form for antiderivatives?

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Is there a general formula for antiderivatives the same way there is for derivatives?So, I know that first-order derivatives can be calculated with the formula:      f    ′    (  x  )  =      lim          h      →      0                  f      (      x      +      h      )      −      f      (      x      )        h  Is there such a limit/standard form for antiderivatives?

Kiana Cantu · Accepted Answer

Step 1No, there is no such a limit expression for antiderivatives directly, mainly because antiderivatives of a function are not unique, and how varied the family of antiderivatives also depends on the connectedness of the domain of the function.Step 2The fundamental theorem of calculus does state that if   f  :  [  a  ,  b  ]  →      R  , then       ∫    a    x    f  (  x  )        d    xis an antiderivative of f, and this does have a limit definition. However, this only works in some circumstances, since it relies on the fundamental theorem of calculus.

auto23652im · Accepted Answer

Step 1If you are looking for a formula to obtain elementary functions, then the answer is no, there isn&#039;t.If you have an elementary function, its derivative is also an elementary function. This is however not true if you go the other way. There are even many relatively simple such functions, for example       e                  x        2             and   sin  ⁡  (  x  )      /    x.Step 2If you are not looking for elementary functions, then for any continuous function f, the function g given by   g  (  x  )  =      ∫    a    x    f  (  t  )  d  t is an anti derivative. Here we choose a and x so that the integral is inside the functions domain.

Is there a general formula for antiderivatives the same way there is for derivatives? So, I know th

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