Integration
Integration is one of the beautiful pillars of calculus. It revolves around the idea of doing the opposite of differentiation, an anti-differentiation. Sounds straight forward right? However, there is an unbelievable connection which revolutionized mathematics entirely! That result is that anti-differentiation is equivalent to the area under a curve. In this video we take a deep dive into integration and explain why it is the area under the curve. Problem Sheet: https://mathacy.com/problem-sheets Timestamps: 0:00 - Intro 1:15 - Inverse Operators 1:45 - Integrating x^n 2:46 - Adding a constant 3:44 - Integrating cos(x) 3:53 - Integrating exponentials 4:10 - Integrating 1/x 5:18 - Area under a curve 6:14 - The link between Area and Integration
Differentiation
Stationary Points (Turning Points)
Integration by parts (visualised)
What is Integration? 3 Ways to Interpret Integrals
Area between two curves – Calculus, Integrals
Derivatives Aren't What You Think They Are
Parametric and Implicit Differentiation (visualised)
Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus
When Math Isn’t Based in Reality
integration by parts, DI method, VERY EASY
Differentiation - The Chain Rule
What is Integration? Finding the Area Under a Curve
Why is calculus so ... EASY ?
The Easiest Integral on YouTube
My new favorite function?
Vectors - The Complete Introduction
What is e and ln(x)? (Euler's Number and The Natural Logarithm)
The function that solves every Integration question | Weierstrass Substitution | tan(x/2)
How Maxwell's Equations Were Discovered
