# Preface to Integration from First Principles

## Integration from First Principles

Foreword: This series is in the form of a booklet. This part of the series is the preface to the booklet. (Use the latest Mozilla Firefox Browser, to see the equations properly.)

By: Chrysanthus Date Published: 1 May 2019

You must not reproduce this document in any form of media (printed paper, book, Internet, etc.). You are free to read the complete document. If you want to teach it, use your own words and examples. If you want a booklet with examples and comparisons between this approach and the traditional/conventional approach of integration, then place an order at forchatrans@yahoo.com. If you want to produce a document from this, for the purpose of teaching, make sure you use your own words and your own examples.

By me,

F. Chrysanthus
(The Discoverer/Inventor)

### Preface Proper

This discovery/invention integrates mathematical functions from first principles. It simplifies integration. Functions which can be integrated, but whose integrals are not known, can now be integrated. In the course of integration from first principles, you can develop/invent your own series, as I have developed/invented.

Anybody who has studied integration can understand this paper.

How, I discovered it: As a teacher, I was looking for the best way to teach one of my daughters, integration. Beginning with the definition of integration, which is:

$∫ a b f ⁡ ( x ) d x = lim ⁡ δ x → 0 ∑ x = a x = b y δ x$

I started by realizing that this statement is not perfect. It should actually be:

$∫ a b f ⁡ ( x ) d x = lim ⁡ δ x → 0 ∑ x = a x = b f ⁡ ( x n ) δ x$

where f(xn) is a particular height from the curve to the x-axis.

I carried on working along side my other duties, and within two months, I produced different function types, taught in the high school.

Continue reading at the next part of the series.

Chrys