The 17 Essential Topics to Master Integration

1

Download the Integration Cheat Sheet Here

2

Integration is the Reverse Process of Differentiation

Integration of Polynomials

The Most Important Integrations to Memorize

Two Challenging Problems

Test Your Learning

3

The 3 Easy Steps for uSubstitution

Two Solved Examples

The 4 important types of uSubstitution problems

Test Your Learning

4

The 2 steps in Evaluating Definite Integrals

Integration is just the Area under a Curve

Simplifying complicated Integrations with Geometry

Two Solved Examples

Test Your Learning

5

Approximating Areas using Rectangles

Left and Right Endpoint Methods

The Trapezoidal Method

Test Your Learning

6

The Formula to calculate Area between Curves

Solved Example: Area Enclosed between Two Parabolas

Integrating Along the Y Axis

Integrating Along the Y Axis to Find Enclosed Areas

Test Your Learning

7

Using Disks to Calculate Volumes

Using Washers to Calculate Volumes of Hollow Solids

Rotation Around the Y Axis

Test Your Learning

8

Calculating Volumes using Thin CrossSections

Test Your Learning

9

The Formula for the Length of a Curve

Integrating with respect to Y to calculate the Length of a Curve

Integrating with respect to Time

Test Your Learning

10

Calculate Position by Integrating Velocity

Calculate Position & Velocity by Integrating Acceleration

Solved Examples Involving Constant Acceleration

Test Your Learning

11

Integrate Powers of sin x & cos x

Integrate Powers of tan x & sec x

Using Double Angle Formulas for Integration

Test Your Learning

12

Integration by Parts in 3 Easy Steps

How to Apply Integration by Parts Twice

How to Simplify Tedious Problems using the Tabular Method

Test Your Learning

13

The Basic Method of Partial Fractions

How to Decompose Repeated Factors

Important Techniques to Factor Polynomials

Partial Fractions for Quadratic Factors

Test Your Learning

14

Reduction Formulas for powers of sin x, cos x, tan x & sec x

Trigonometric Substitution

Test Your Learning

15

Separation of Variables

Exponential Models of Growth and Decay

How to Draw Slope Fields using Isoclines

Test Your Learning

16

How to Convert between (x,y) and (r, theta) Coordinates

How to Calculate the Length of a Polar Curve

How to Calculate the Area Enclosed in a Polar Curve

How to Calculate the Area Enclosed between Two Curves

Test Your Learning

17

Monotonic & Bounded Sequences

Geometric Series

Test Your Learning

18

Using Taylor Series to Approximate Functions

Using Maclaurin Series to Approximate Functions

Test Your Learning
