Integration in Python

Making Your Academic Life Much Easier with Python — #PySeries#Episode 21

Hi, in this episode we gonna solve some integration using Python.

SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python.

This is my first attempt at working integrals in python, since I have some difficulties in algebra :)

Fundamental Calculus Theorem:

Now, from the calculation, we know that the area defined is given by:

To start off on our journey, open your Colab Notebook.

Let’s get it on!

First, import these libraries:

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import sympy as sy

Now please answer these 5 question (just 5:)

01#PyEx — Python — Definite Integral:

Calculate the integral of the function bellow and make the graph: 

Fig 1. Graph of exercise 01

02#PyEx — Python — Python — Definite Integral:

Calculate the integral  of the function bellow and make the graph:

Fig 2. Graph of exercise 02

03#PyEx — Python— Definite Integral:

Calculate the integral  of the function bellow and make the graph:

Fig 3. Graph of exercise 03

04#PyEx — Python — Python — Definite Integral:

Now the hard part:
Calculate the definite integral  of the function, first by hand, them, using Python lambda function, and solve this:

05#PyEx — Python — Python — Definite Integral:

The hard part, again:
Given these 2 fuctions f(x)& g(x):

Fig 4. Graph of exercise 05; Blue — f(x); Orange- g(x)

Calculate the area between the two functions and present a graph;)

From now on it’s up to you!

If you are feeling rusty, see the answer in the notebook below, prepared just for your enjoyment!

If you find this post helpful, please consider to subscribe to the Jungletronics for more posts like this, and much, much more…

Until next time!

I wish you excellent day!

Be safe!

Cheers!

Colab Notebook Anwers link:)

Google Drive link:)

Google Colab Notebooks are here:

Credits & References

Integrating functions in python by kitchingroup.cheme.cmu.edu

Taking Derivatives in Python by Dario Radečić

SymPy by SymPy

Calculate Derivative Functions in Python by Erik W

Higher Order Partial Derivatives

Integration by calc-again.readthedocs.io

MathJax

Markdown Guide

LaTeX/Mathematics - Wikibooks, open books for an open world

Cálculo com Python by phkonzen.github.io

Fundamental theorem of calculus by wikipedia.org

Introduction — What is Symbolic Computation? by docs.sympy.org

Sympy : Symbolic Mathematics in Python by scipy-lectures.org

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