Integration & Antiderivatives

Emily Davis

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Next Topic - Derivatives & Antiderivatives

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Study Guide Overview

This study guide covers indefinite integrals, including their definition as the antiderivative of a function plus a constant of integration (C). It explains the relationship between integration and differentiation as inverse operations, the importance of the constant C, and provides practice questions. Key terms covered include: antiderivative, constant of integration, and indefinite integral. The guide also emphasizes the concept of a family of antiderivatives.

#Indefinite Integrals

#Table of Contents

What is an Indefinite Integral?
Why Do We Need the Constant of Integration?
Practice Questions
Glossary
Summary and Key Takeaways

#What is an Indefinite Integral?

Definition: The indefinite integral of a function $f(x)$ is denoted by $\int f(x) , dx$ .

$\int$ is the mathematical symbol for 'integrate'.

Key Concept

When we find the indefinite integral of $f(x)$ , we are integrating the function.

The $x$ in $dx$ indicates that we are integrating $f(x)$ 'with respect to $x$ '.

#Formula for Indefinite Integral

The indefinite integral is defined as:

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

Where $F(x)$ is a function such that $F'(x) = f(x)$ .
$C$ is any constant, known as the **const...

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Previous Topic - Critical Points of Implicit Relations Next Topic - Derivatives & Antiderivatives

Question 1 of 9

What does the indefinite integral, denoted by $\int f(x) , dx$ , represent? 🚀

A single unique function $F(x)$

A family of functions $F(x) + C$ , where $C$ is any constant

The derivative of the function $f(x)$

The slope of the tangent line to $f(x)$