This morning, I had an animated discussion in math class with our professor about whether memorizing certain integrals (natural log in particular) is a good idea. The professor stated that it’s important to know the general steps of the process through which you can find a particular integral, and I agree. She also said something that really seemed counterintuitive to me.
“Why memorize when you can compute?”
From my point of view, the class had recently made sure to memorize (as instructed) an assortment of trig integrals and derivatives. We’ve begun to memorize calculus-style formulas for area. We memorize these because no one wants to reinvent the wheel.
From her point of view (as I understand it), it’s good to know how these derivatives, integrals, and formulas are derived—know where they come from. And it’s silly to try to memorize the solution to every specific multiplication problem (58×27 for example) when you can simply learn the general solution to all multiplication problems and thus understand the process.
But we still memorize the multiplication table. We’ve done those numbers so many times that we don’t have to think about them—most of them anyway. I suppose the reason the Professor and I had a little scuffle this morning is because she thought my integral was a 58×27, and I thought it was a 2×10.
In any event, I never meant to memorize the integral of natural log. It happened while I was looking the other way, engrossed in a puzzle of equations. That’s the best kind of memorization, the kind that lasts and that you don’t notice happening. It’s experiential, quite painless, and results in intuitive understanding.
There’s also one other “best” way to memorize, quite opposite to this approach, but that’s for another day.