What they don’t teach you about integration at school

Extract

As a mathematician involved in teaching students whose abilities range from barely numerate to MSc level, I am frequently concerned by the lack of basic understanding exhibited by pupils regarding the subject of integration. Invariably the most practical way of introducing the subject of integration is by thinking of it as “anti-differentiation”, so that the problem is to pick a function which “when differentiated will give what you first thought of”. This of course may be allied to the idea of the area under a curve to give the student a conceptual feel for the subject. Usually when simple rules for the integration of powers, trigonometric functions, exponentials, logarithms and so on have been mastered, the next step is to introduce the standard methods for proceeding.