Integration Playlist
Take a thorough stroll through one of the most beautiful parts of the calculus trail! This playlist will teach you all the fundamentals of integration from the area under the curve to integration by parts. This playlist is aimed at students studying A-level (11-12th grade) and beyond. You’ll find a problem sheet at the end of each video to help you achieve your best!
Integration introduction
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.
Integration by Parts
Integration by parts is one of the most useful tools for finding integrals! In this video we cover what it is, how it works and we also show what is VISUALLY happening!
Integration by parts is the product rule for Integration. It allows us to find the integral of functions multiplied together and it is a super interesting solution to a geometrical problem! Check out the problem sheet below!
Integration by substitution
Integration by substitution is one of the most powerful tools for combating integrals! It allows us to transform a difficult integral into a significantly easier one. In this video we visually show what actually happens when you perform a substitution and how to properly use integration by substitution.
Check out the problem sheet below!
The Ghost Substitution
The Ghost Substitution (commonly known as the Weierstrass or Half-Angle Tangent Substitution) is one of the 'sneakiest substitutions' in mathematics. The Ghost Substitution utilizes a very clever and useful property about trigonometric functions which allows us to solve complex calculus related problems. In this video, we visually explain how we can intuitively define the circle using the Ghost Substitution and how we can use the substitution in Integration - perhaps it's most important use!
Check out the problem sheet below!
