Recurrence Relations (Reduction Formulas)

Recurrence relations, or reduction formulas, are part of the Further integration topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-04). This subtopic derives and uses recurrence relations that express an integral \(I_n\) in terms of an integral with a lower index, usually by applying integration by parts.

Students and teachers will cover how to derive a reduction formula and then use it repeatedly to evaluate an integral such as \(\displaystyle I_n = \int_0^{\pi/2} \sin^n x\,dx\) for a particular \(n\) — a demanding skill in the HSC Extension 2 course.