In this post, we interpret the definite integral \int_{a}^{b} f(x) dx as area under the curve y = f(x) if f(x)>0 , and recognise the definite integral as a limit of sums of the form \sum_{i} f(x_{i}) \delta x_{i} . This syllabus dot point is a part of the QCE Maths Methods course under the topic Integrals and sub-part Fundamental Theorem of Calculus and Definite Integrals.
Definite Integrals
Part 1: Sign and symmetry
Part 2: Dissection and direction
Part 3: Addition
Part 4: Piecemeal functions
