Differentials and integrals: Indefinite integrals
Antiderivatives of standard functions
The search for antiderivative of a given function on an interval, that is, the search for a function for a given function on an interval with the property that , is called finding the primitive or integrating. The following equality is valid for this primitive function and any and in
Every antiderivative (also called primitive) of on can be written this way. One often denotes such a primitive function of without lower and upper limits in the format
and then one callls it an indefinite integral. The indeterminacy lies in the fact that antiderivative of is only uniquely determined up to a constant of integration. A simple example of an indefinite integral on is
where the constant of integration is denoted with the letter . Many mathematical software programs such as the computer algebra systems Maple and Mathematica do not mention the constant of integration and provide only one primitive function.
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Integration as the reverse of differentiation (34:14)
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