Volume of Solids of Revolution

Summary Rotating about the x axis, Volume of Revolution: Rotating about the y axis, Volume of Revolution: Definite Integrals Formula  We know that definite integrals can help us figure out areas underneath the curves. Recalling the formula for definite integrals from the article ”Integration” : Similarly, pretty much using the same principle we can work … Read more

Area under a curve

Summary Area under a curve can only be calculated if the integral is definite. It must have limits. We must be aware of the three common scenarios when working out the areas under the curves: Area Under the Curve Find area between a curve, the x axis and the line x = a and x … Read more

Differentiation of Trigonometric Functions

Summary Remember these derivatives of the trigonometric functions: Differentiation of sin(x) and cos(x) To begin with, we know that differentiation is a method to find the gradient of a curve. Rule of differentiation is if , then  . However in this article we will focus entirely on differentiation of trigonometric functions. Consider the graph of … Read more

Trapezium Rule

Summary Trapezium rule can only be applied to Definite Integrals. Area under the curve is divided into equally spaced intervals forming a trapezium. Trapezium Rule only provides an estimate area of under the curve. The formula given is: where Definite Integrals Let’s start by briefly recalling the definite integrals from the article ”Integration”. Definite Integration … Read more


Summary Differentiation is a method to find the gradient of a curve. When differentiating a function, always remember to rewrite the equation as a power of x. This makes it easier to differentiate. Differentiation formula: if , where n is a real constant. Then . Derivative of a constant is always 0. Basic Rules of … Read more


Summary Indefinite Integral:      The ”C” means any number. This is the constant of integration. Definite Integral:      Area under the curve:      Area between a curve and a line      Approximate area using trapezium rule: Where and . Integration is the inverse of differentiation. It is the general formula for the Area under the graph … Read more