Primitive. Indefinite integral
Indefinite integral. Constant of integration.
Primitive. A continuous function F ( x ) is called a primitive for a function f ( x ) on a segment X , if for each
E x a m p l e . The function
a primitive for the function
) = 3
interval ( - , + ) , because
It is easy to check, that the function x 3 + 13 has the same derivative 3 x 2 ,
so it is also a primitive for the function 3 x 2 for all x ( - , + ) .
It is clear, that instead of 13 we can use any constant. Thus, the problem of finding a primitive has an infinite set of solutions. This fact is reflected in the definition of an indefinite integral:
of a function
on a segment
This is written as :
where C – any constant, called a constant of integration .