Reduction Formulae (AQA A-Level Further Maths): Flashcards

Relates $I_n$ to $I_{n-1}$ and/or $I_{n-2}$

$\int u \frac{dv}{dx} dx = uv - \int v \frac{du}{dx} dx$

Avoid repeated integration by parts; derive formula once

Recursive relationship

Part containing power $n$ so power reduces when differentiated

Both definite and indefinite integrals

$I_n = -nI_{n-1}$

$I_n = \frac{n-1}{n}I_{n-2}$

Reach $I_0$ or $I_1$, evaluate directly, substitute back

Even powers reduce to $I_0$, odd powers to $I_1$