called the indefinite integral of f to denote the family of all antiderivatives of f. Linearity: Z (af(x) + bg(x)) dx = a Z f(x) dx + b Z g(x) dx.

This implies that the integral of f(x) is not definite. By virtue of this property F(x) is called the indefinite integral of f(x).

12.2.1 Basic Properties of Indefinite Integrals. Since integration is the reverse process of differentiation, we can derive some basic properties of indefinite.

In this Chapter, we shall confine ourselves to the study of indefinite and definite integrals and their elementary properties including some techniques of ...

Use basic integration rules. Introduction. In this lesson we will introduce the idea of the antiderivative of a function and formalize as indefinite integrals.

5.3 Properties of indefinite integral. Next we shall prove three properties of the indefinite integrals and use them to integrate some functions. Property 3.1.

It discusses: 1) Basic properties of indefinite integrals such as constants of integration and integrating sums of terms. 2) Standard formulas for integrating ...

According to the theorem above every continuous function has an antiderivative. However, it might not al- ways be possible to find its explicit formula.

This implies that the integral of f(x) is not definite. By virtue of this property F(x) is called the indefinite integral of f(x) . Page ...

In this lecture, we define an antiderivative of a function and study its properties. We will define the indefinite integral of a function as its general ...