11th Grade - Antiderivative

11th Grade lesson

3 - Antiderivative

Definition of an antiderivative

This part of the site is useful for the next page : the integrals.
The antiderivative (or antiderivative) of a function f, is a function F such as F' = f.
A function has many antiderivatives which all dissent from a constant C. Here are two example of antiderivatives of functions :
antiderivative de function antiderivative de function
If you derivate the function F, you find f.
In general :
antiderivative function puissance

If u is a function, an antiderivative of antiderivative function puissance is antiderivative function puissance, and an antiderivative of antiderivative function logarithme is antiderivative function ln. For the calculation, you also have to know that the antiderivative of a sum of functions is equal to the sum of the antiderivatives of the functions, and that if alpha is a real number, an antiderivative of antiderivative produit is antiderivative produit.

How to calculate an antiderivative

exemple antiderivative exemple antiderivative

In the examples above, you simply apply the general formula of a antiderivative of a power of x. Below we are going to use the formulas of the exponential and logarithm functions, and to do this we 'll have to modify f.
exemple antiderivative compliquée
Suppose calculation antiderivative, then we have calculation antiderivative. Above we managed to express f functions of u and its derivative. Thus finally :
resultat calculation antiderivative

Last example,
exemple calculation antiderivative

Suppose methode calculation antiderivative, then calculation antiderivative and hence : antiderivative function.

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The antiderivatives

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