# List of Notes - Category: Antiderivative and Indefinite Integral

## Concept of Antiderivative and Indefinite Integral

In the Calculus I (Differential Calculus) our main purpose was to find derivative of given function.

But often we need to solve inverse task: given a function f(x) find function F(x) whose derivative is f(x). In other words, we need to find function F(x) such that F'(x)=f(x) .

## Properties of Indefinite Integrals

Following properties of indefinite integrals arise from the Constant Multiply and Sum rules for derivatives.

Property 1. If a is some constant then int a*f(x)dx=a int f(x)dx +C. In other words cosntant can be factored out of integral sign.

## Table of Antiderivatives

Below is a short list of functions and their general antiderivatives (we will give more complete table later).

Note that int f(x)dx=F(x)+A and int g(x)dx=G(x)+B where A and B are arbitrary constant.

## Area Problem

Suppose that we are given continuous function y=f(x) on [a,b] such that f(x)>=0 for all x in [a,b].

We want to find area S that lies under curve f(x) and bounded by lines x=a, x=b and x-axis.