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#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# Length of a Curve

A major use of derivatives and integrals is finding the length of a curve. There's a formula for this:

Figure 11.1: Formula to calculate the length of a curve

The preceding formula contains an integral and a derivative. To find the length of a curve, we'll need both our derivative and integral functions. Copy and paste them into your code if you don't have them yet:

```from math import sqrt

def derivative(f,x):
"""Returns the value of the derivative of     the function at a given x-value."""
delta_x = 1/1000000
return (f(x+delta_x) - f(x))/delta_x

def trap_integral(f,a,b,num):
"""Returns the sum of num trapezoids     under f between a and b"""
width = (b-a)/num
area = 0.5*width*(f(a) + f(b) + 2*sum([f(a+width*n) \      ...```