Integrals

Integrals are the heart of Integrity. My original reason for creating this site was to store and archive all the integrals I’ve written.

What kinds of integrals go on Integrity?

I started writing integrals for my school’s Integration Bee. I think I ended up writing about 300 questions, but most of these were fairly formulaic or trivial, unworthy of going on Integrity.

What do I need to know?

It’s painfully nontrivial to pinpoint a precise ‘threshold’ for what level of integration ability is required, or provide a comprehensive ‘specification’ for what knowledge you need. The difficulty and style of integrals on Integrity varies hugely, and of course everyone will perceive them differently depending on their exposure and experience.

I will say that if you are confident with the integration taught in A-level Further Mathematics^↗,¹ the basic principles you learn there will leave you in a good spot for tackling Integrity’s integrals. The cheatsheet should also act as a useful checklist for algebra and calculus you should be familiar with.

TIP

Integrals that may require more advanced knowledge will be tagged with ELITE.

Now, my integrals are quite different in purpose, style and difficulty to A-level integrals – they’re intricate puzzles designed to make you think and ponder, more than examination questions trying to assess your understanding of integration. It’s certainly great to challenge yourself, and I love tackling tough integrals I have no idea how to solve, but if you’re not that comfortable yet with how to integrate, I would recommend practising with easier, more formulaic problems first before tackling Integrity.

And remember, integration is not a lone topic – polynomials, trigonometry, exponentials – they’re all very much relevant and helpful! So while you’re building up your integration ability, remember to not neglect other areas of mathematics.