Integrating using Trigonometric Substitutions The integrals covered in this revision note are based on the standard results and These are given in the formulae booklet How do I know when to use a t...
Differentiating Inverse Trig Functions What are the inverse trigonometric functions? arcsin, arccos and arctan are functions defined as the inverse functions of sine, cosine and tangent respectivel...
Integrating with Partial Fractions What is meant by partial fractions with quadratic denominators? For linear denominators the denominator of the original fraction can be factorised such that the d...
Mean Value of a Function What is the mean value of a function? The mean value of a function may be thought of as the ‘average’ value of a function over a given interval For a function f(x), the mea...
Improper Integrals What are improper integrals? An improper integral is a definite integral where one or both of the limits is either: Positive or minus infinity A point where the function is undef...
Adding and Subtracting Volumes Why might I need to add or subtract volumes of revolution? As with the area between a curve and a line or the area between 2 curves, a required volume may be created ...
Volumes of revolution around the x-axis What is a volume of revolution around the x-axis? A solid of revolution is formed when an area bounded by a function (and other boundary equations) is rotat...
Differentiating Hyperbolic Functions What are the derivatives of the hyperbolic functions? These are given in the formulae booklet You can prove them by differentiating the definitions involving e ...
Hyperbolic Identities & Equations Are there identities linking the hyperbolic functions to the circular trig functions? Yes - these can be seen using de Moivre's Theorem to write Compare these ...
