"Exam condition"

An idea during study week.

It might be easy to integrate the function
f(x) = (x-3)(x²+1).


But what about its reciprocal 1/f(x) ?
(I couldn't type it out easily; so I described it in words instead.)

Maybe we should give it a few moments of thought.

While doing my usual study/revision this week, I realized - like numerous times before this - that learning, or input, can actually be really fun. Making mnemonics, drawing mind maps, producing charts and tables to organize newly-learned materials, etc., could be quite addictive. It also has a lag tendency, unfortunately. It's like a comfort zone of learning where there's nothing else that I'd rather be doing.

And the purpose of this study week is for preparation for next week's end-of-semester exam. The assessment is the real output. Not the mnemonics, mind maps, charts, tables, etc. They do help, but if I can't reproduce them within the exam time limit, then I wouldn't score excellent marks. In fact, I've experienced that the act of deciding which mind map is relevant for a question itself actually consumes so much time! It's so different from the input phase. The writing process is accelerated. The thinking process must be spontaneous. And it involves high-precision work.

Which brings to my idea for today.

The exam condition is like a pressure cooker. Time is very limited. Every second is utilized for the cooking process.

And, by the way, I tried solving the above problem (1/f(x)) by some substitution step, which was futile. A friend whom I asked told me that I need to use partial fractions and then use inverse trigonometric integration for one of the terms.

No way could I have done it efficiently under exam condition, because that would be cheating.


Happy SWOT VAC.