The vast majority of questions on Integrity are integrals. Some of the stuff we’ll talk about may vary slightly between question topics, but broadly speaking they will apply to all of them.
Shards
These are unique identifier codes for every question. See Shards for more.
Tags
In the question browser you’ll see blue tags under each question, showing the topics / categories they fall into. They’re pretty self-evident – the reason for having them there is more for searching and filtering. For instance, if my friend asks for hyp trig integrals, I can just go to Integrals and filter by the HYP TRIG tag.
For details on what every tag means, see Tags.
Methods
Via search filters you can also show and filter by method tags, in orange. These reveal what methods the question will involve, so are somewhat spoilers – hence they’re hidden by default. You may find them helpful if you want to practise a particular topic.
Hints
Most questions will have a few hints. These are intended to nudge you in the right direction if you’re stuck on a question, or act as confirmation that you’re along the right path, so that you don’t have to spoil the problem by knowing the answer. I love tackling tough problems, but staying stuck with no indication of where to go can suck. Having a few hints that don’t fully give away the solution can be quite nice.
Individual hints are hidden by default when you expand the “Hints” section so that you don’t accidentally see any you don’t want to, and you can choose to expand them at your discretion.
Why do questions have different numbers of hints?
3 is the standard. Fewer most probably just means it’s difficult to provide hints without giving the entire question away. More, and there’s a good chance the question’s either very tough, obscure, long, or all 3.
I’m really confused by the hint.
Naturally, the best hints are those provided by someone watching you solve the problem, where they can see your thought process, what you’ve tried before, where you’re headed, etc. They know how much progress you’ve made, and can tailor the hint to give you just the right info to get unstuck. This is a bit nontrivial to do via a website, so the hints may not always coincide with what you’ve done.
Also, remember that many problems, especially integrals, can have more than 1 possible solution. The hints will lead to the canon solution you’ll find on the page, but your alternative method may well just work.
Alternate Solutions
Many questions, especially integrals, may have multiple possible solutions and even answers. The canon solution (under the Solution section) I provide may not always be the simplest or most elegant – it’s probably just the one I had in mind when writing the question. For questions where I notice there’s a noteworthy alternative route(s), you’ll find it under the Alternates section.
If you’ve found a really cool alternative solution and would like to let me know, feel free to just drop an issue on GitHub – I’d love to see!