3.7 Integration
Integration
The basics Video tutorial 1
Areas under a graph and between curves
Definite integration (similar to above)
Finding the equation of a line (finding C) Part 1
Finding the equation of a line part 2
Harder examples of trig functions (reverse chain rule )
Integrating Trig functions with powers (using double angles). Video 1 Video 2
Integration by inspection (reverse chain rule). Video 1 Video 2 using e^ Using ln x video 3 Hard example Video 4
Integration by substitution Video tutorial 1 Video tutorial 2
A collection of all different types again just from a different source, inc trig functions, using trig identities and more. Worth watching all.
When to use what rule examples
Kinematics in integration. Video 1 Video 2
Numerical methods for integration
Mid ordinate rule. Video tutorial. Slides explanation
Trapezium rule. Video tutorial. Slides explanation
Differential equations
(before doing the modelling questions, you have to understand proportion, direct and indirect. Watch this, read these Notes, do these questions & answers)
The order in which I teach differential equations is the same as the order in which the videos are posted. NCEA tend to use the modeling and hence the last few videos are very important.
The first set really cover integrating equations to make a general solution. Be aware that we do not use implicit differentiation so do not panic just watch it.
Tutorial 1. Tutorial 2 Tutorial 3
Tutorial on setting up a differential equation from a model. Tutorial 1, Tutorial 2
Newtons laws of cooling. Tutorial