An integral is the reciprocal process to differentiate. 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 a 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 on both the horizontal axis and the vertical lines defined as x=a and x=b.
It is that set of primitives that a function can have. A primitive function or anti-derivative 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 admits an infinity, the difference between primitives is identified as a constant C. That is, if F1 and F2 are primitives of f then F1=F2+C. this constant is known as the constant of integration. The indefinite integral is the inverse of the differentiation.
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. This is the inverse of the derivation.
- Definite integration is one that is applied to locate the area under a curve by integrating a function over a given interval that is different from 0.