Integrals can be classified into two groups, definite and indefinite integrals. Defined ones are those that allow you to determine the value of areas bounded by curves and lines, while an indefinite integral is one that contains the set of infinite primitives or antiderivatives of a function.
An integral is a reciprocal process to be derived. This means that for a function f (x), it looks for those functions F (x) that, when derived, lead to f (x). This means that F (x) is primitive or integral of f (x). Definite integrals are those that allow determining the value of areas bounded by curves and lines when an interval (a, b) is given for a point x that defines a function f (x) greater than or equal to zero at that point.
The definite integral of a function between points a and b is the area of the portion of that plane that is bounded by the function both on the horizontal axis and the vertical lines defined as x = a and x = b.
It is that set of primitives that can have a function. A primitive or anti-derivative function of a function f is a function F whose derivative is f. The condition that f must fulfill to admit primitives on an interval is that said dry function continues in the mentioned interval.
If the function f admits a primitive in an interval it admits infinity., The difference between primitives is identified as a constant C. That is, if F1 and F2 are primitives off then F1 = F2 + C. this constant is known as the constant of integration.
The indefinite integral is the inverse of the derivation.\
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Differences between definite and Indefinite Integral
- The indefinite integral seeks to obtain the primitive of a function. That is the one whose derivative is the given function. It is the inverse of the derivation.
- Definite integration is one that is applied to locate the area under a curve by integrating a function between a given interval that is different from 0.