Further MathematicsCode 9231
Integration
What this topic asks you to be able to do
- integrate hyperbolic functions, identify integrals of the forms 1/(√(a² - x²)), 1/(√(a² + x²)) and 1/(√(x² - a²)), and perform integration of associated functions by making trigonometric or hyperbolic substitutions where suitable
- derive and apply reduction formulae to work out definite integrals
- understand the manner in which rectangles can give an approximate value for the area beneath a curve, and apply rectangles to estimate, or to establish bounds on, the area beneath a curve, or to obtain inequalities or limits involving sums
- apply integration to obtain the lengths of arcs for curves given by equations in Cartesian coordinates, including where a parameter is used, or in polar coordinates
- apply integration to find the surface area of revolution when a curve with a Cartesian equation, including one given in terms of a parameter, is rotated about one of the axes