Calculus and Definitions of Its Concepts
Indefinite integration
Indefinite integration is the act of reversing any process of differentiation. It is the process of obtaining a function from its derivative. It is also called anti-derivative of f. A function F. is an anti-derivative of f on an interval I, if F'(x) = f (x) for all x in I. A function of F (x) for which F'(x)=f (x), this means that for every x domain of f is said to be an anti-derivative of f (x)
The anti-derivative of a derivative is the original function plus a constant. In most cases indefinite integral is denoted by ? symbol which is called the integral sign, and f (x) is referred to as the integrand. In most cases in indefinite integration the constant C. is always zero this means that any constant can be added to it and the corresponding function bear the same integral.
An indefinite integral is in the form:
If the bounds are not specified, then the integral is indefinite, and it no longer corresponds to a particular numeric value. There is a simple geometric interpretation for the fact that any two anti-derivatives of the same continuous f differ by at most a constant. When we say that F. And G. are both anti-derivatives of f we mean that F'(x) = G'(x) therefore the slope of the curve y = f (x) is the same as that of y = G (x) in other words the graph of G (x) is a vertical translation of the graph F (x) (Bradley et al.,.2000)
Indefinite integral differs from definite integral in that the indefinite integral exists it usually exists as a real value, while the values vary according to the constant.
Definite integration
The formal definition of a definite integral is stated in terms of the limit of a Riemann sums. We will introduce the definite integral defined in terms of area. Whereas the indefinite integration analyzes...
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