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# Integral Calculus

## Take the next step on the calculus journey with integrals and sums.

In a sense, differential calculus is local: it focuses on aspects of a function near a given point, like its rate of change there. Integral calculus complements this by taking a more complete view of a function throughout part or all of its domain.

This course provides complete coverage of the two essential pillars of integral calculus: integrals and infinite series. By the end, you'll know their core principles and how to apply them to problems in geometry, probability, and physics.

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1. 1

### Introduction

The core of integral calculus.

1. #### Calculating Distance

Find your way to Riemann sums through a simple motion problem.

2. #### Different Problem, Same Idea

See how Riemann sums crop up in many different places.

3. #### The Definite Integral

Leverage your understanding of Riemann sums to master the basic ideas of integration.

2. 2

### Integration Techniques

The essential toolkit, from the fundamental theorem to substitutions.

1. Included with

#### First Calculations

Make the connection between limits, Riemann sums, and definite integrals.

2. Included with

#### The Fundamental Theorem of Calculus

Solidify your complete comprehension of the close connection between derivatives and integrals.

3. Included with

#### Integrating Polynomials

Begin to unravel basic integrals with antiderivatives.

4. Included with

#### Substitution

Reverse the chain rule to compute challenging integrals.

3. 3

A medley of integration techniques that no professional can do without.

1. Included with

#### Integration by Parts

Combine derivative rules to reshape a definite integral into something simpler.

2. Included with

#### Basics of Partial Fractions

Learn to break rational integrals down into simpler parts.

3. Included with

#### Trigonometric Integrals

Simplify tricky trig integrals with Euler's formula.

4. Included with

#### Trig Substitution

Uncover powerful integrals through trigonometry.

4. 4

### Integral Applications

Use integrals to solve crucial problems in math and science.

1. Included with

#### Area and Probability

Dive into some real-world applications of integrals.

2. Included with

#### Calculating Volume

Construct volume integrals for a variety of 3D objects using disks, washers, and shells.

3. Included with

#### Arc Length and Surface Area

Apply integrals to geometry and explore the paradoxical shape of Gabriel's Horn.

4. Included with

#### Integration in Physics I

Go beyond geometry and put integrals to work in physics problems.

5. 5

### The Idea of Infinite Sums

The fundamental concepts of sums without end.

1. Included with

Learn about infinite series through a legendary footrace.

2. Included with

#### Sums and Sigma Notation

Master the language of sums both finite and infinite.

3. Included with

#### Secret Identities

Expose familiar functions as infinite sums in disguise.

6. 6

### Infinite Series

Convergence tests for infinite sums and their applications.

1. Included with

#### Converging Sums

What does it mean for a sum to converge?

2. Included with

#### Ratio and Root Tests

Exploit the geometric sum to create brand new convergence tests.

3. Included with