Review/revision
Differential Equations HL - Integrating Factor
On this page, we will look at another type of differential equation: first-order linear differential equations of the form \displaystyle \dfrac{\mathrm{d}y}{\mathrm{d}x}+P(x)y=Q(x), which can be solved...
Review/revision
Differential Equations HL - Separable Variables
If you want to describe the world around you, be it the forces acting on a body, the growth of a virus or the temperature of the coffee in your cup, you will be dealing with differential equations. On...
Review/revision
Integration by Parts
Integration by parts is a method of integration that we use to integrate the product (usually!) of two functions. The aim is to change this product into another one that is easier to integrate. Although...
Review/revision
Integration by Substitution HL
Integration by substitution or U-substitution is a method that will help you integrate many different functions. By changing the variable of the integrand, we can make an apparently difficult problem...
Review/revision
Integration by Substitution SL
Integration by substitution or U-substitution is a method that will help you integrate many different functions. By changing the variable of the integrand, we can make an apparently difficult problem...
Review/revision
Volume of Revolution HL
On this page, we will learn how to find the volume generated by rotating a region about the x-axis and the y-axis. The formulae for these are not difficult to use. The difficulty often comes with applying...
Review/revision
Area between Graphs HL
On this page, we'll look at how we can use integration to find areas. This is a really common question in examinations. The technique is not too hard, but there are just a couple of pitfalls to avoid...
Review/revision
Area between Graphs SL
On this page, we'll look at how we can use integration to find areas. This is a really common question in examinations. The technique is not too hard, but there are just a couple of pitfalls to avoid...
Review/revision
Definite Integration
Integration is sometimes called antidifferentiation, as it is the opposite process of differentiation. When we find an indefinite integral, we find a function with an arbitrary constant, C. Whereas, when...
Review/revision
Standard Integrals HL
In this page, we will look at some of the standard integration techniques that you need to know about involving x^n, \sin x, \cos x, \dfrac{1}{x}, e^x, a^x, \dfrac{1}{a^2+x^2}, \dfrac{1}{\sqrt{a^2-x^2}} and...