Q. 10 - Calculus

Question

Notation: Describe the meanings of each of the following mathematical expressions or how they are commonly used in this chapter:   

$\int f\left(x\right)dx$

Step-by-Step Solution

Answer

The indefinite integral of a continuous function f is defined to be the family of antiderivatives,

$\int f\left(x\right)dx=F\left(x\right)+C,$

where F is an antiderivative of f, that is, a function for which $F\text{'}=f.$

Step 1. Given information.

We are given an expression,  

$\int f\left(x\right)dx$

Step 2. Defining the expression

The indefinite integral of a continuous function f is defined to be the family of antiderivatives,

$\int f\left(x\right)dx=F\left(x\right)+C,$

where F is an antiderivative of f, that is, a function for which $F\text{'}=f.$