dx = du / cos(x)

[tsukikage]

To math-y types:

If you're doing a u-substitution in an integral, just how un-Kosher is is to, as part of showing your work (and/or leaving yourself a paper trail), explicitly list dx in terms of du in preparation for "substituting" the du-containing equivalent to dx. For example, if I'm integrating sin(x)*cos(x) dx, and let u = sin(x) => du = cos(x) dx, is it then completely improper to continue with "=> dx = du / cos(x)", then substituting this for dx as u*cos(x) (du / cos(x)) = u du? I had my professor check that I'm showing enough work on my calc quiz due tomorrow, and he was adamant that I shouldn't have all u terms and x terms on separate sides at all times, and obviously he grades my quizzes and tests so I'll do what he says, but I could have sworn that saying dx = du / cos(x) was totally acceptable in either Math 1471H or 1271 (it all blurs together), at least in intermediate steps just to help yourself along.

Mmmm, really hoping I can finish my quiz before it's time to get up tomorrow. I seriously don't look forward to the idea of pulling two nighters in a row, and even less the idea of taking a "nap" and not having enought time to finish my quiz.

ETA: "They were a little slower to invoke the Prime Directive, and a little quicker to pull their phasers. Of course, the whole lot of them would have been booted out of Starfleet today." So very true. I like that they're actually addressing the complete difference in mood between TOS and subsequent Trek series.

Comments

[akaneko.livejournal.com]

While the recent Star Trek was most notable in giving itself a canonical excuse to totally break with the established canon howsoever it pleases, I think the general "we are space cowboys and we are going to punch things now!" feel to many of the scenes was quite true to the original. XD

[tsukikage85.livejournal.com]

True dat.