zuai-logo

Riemann Sums & Definite Integrals

David Brown

David Brown

5 min read

Listen to this study note

Study Guide Overview

This study guide covers the Fundamental Theorem of Calculus, exploring both the First and Second Fundamental Theorems. It explains their definitions, theorem statements, and provides a worked example and practice questions. Key terms such as antiderivative, continuous function, definite integral, and accumulation function are defined in a glossary. The guide emphasizes the connection between differentiation and integration.

Fundamental Theorem of Calculus

Table of Contents

  1. Introduction
  2. First Fundamental Theorem of Calculus
  3. Second Fundamental Theorem of Calculus
  4. Worked Example
  5. Practice Questions
  6. Glossary
  7. Summary and Key Takeaways

Introduction

Key Concept

The Fundamental Theorem of Calculus is a crucial concept in calculus that links the concepts of differentiation and integration. It is divided into two parts:

  1. The First Fundamental Theorem of Calculus
  2. The Second Fundamental Theorem of Calculus

First Fundamental Theorem of Calculus

Definition

The First Fundamental Theorem of Calculus connects antiderivatives with the value of definite integrals. This theorem provides a straightforward method for evaluating definite integrals.

Theorem Statement

If ff is a function that is continuous on th...

Previous Topic - Accumulation FunctionsNext Topic - Properties of Definite Integrals

Question 1 of 8

Evaluate the definite integral: ∫023x2,dx\int_{0}^{2} 3x^2 , dx 🚀

6

8

12

4