# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

Author Message
dethwing
DeTheeThaw

 Posted: Sat Feb 04, 2012 6:23 pm    Post subject: 1 So a few nights ago, I was tutoring a calculus student in a u-substitution problem. I won't go into all the details, but basically the part I want to ask about was this. du = 2xdx And there was an "x dx" in the problem. In order to do this, do you: 1. Get du/2 = xdx , and then replace both at once 2. Get du/(2x) = dx, and then replace just the dx, canceling the x/x. Now, I was taught to do it the first way, so I got thrown off a bit when my student starts dividing by x, but then I saw what was going to happen and let it go. So I was just curious, is this a newer way of doing it? Is it just a matter of the text/teacher?
Zag
Tired of his old title

 Posted: Sat Feb 04, 2012 7:33 pm    Post subject: 2 Neither approach is wrong. One is a little cleverer and faster, but a fundamental approach of wanting to remove the dx from the other problem, so solve for it in this one and substitute is always going to yield a correct result. If you happen to notice that there is more in the original problem you can substitute for in one step, that's fine, too; but one might waste more time looking for that sort of thing than benefit from the times finding it. Of course, when the x is something more complex, that you have to take some pains to construct in order to make the substitution work cleanly, it's nicer to be more ready to use your approach. On the other hand, it is never strictly necessary.
Trojan Horse
Daedalian Member

 Posted: Sun Feb 05, 2012 1:07 am    Post subject: 3 As Zag said, both methods are correct. I greatly prefer the first one, though. I don't want my students to get into the habit of replacing dx with a "mixed expression" like du/2x. What happens when they come across a problem where a u-substitution does not work, such as integrating dx/(x^2+4x+3)? I fear they would try the substitution, getting an expression involving both x and u... and then they'd shrug, and just keep on going with the problem. No matter how many times I tell my students, "you have to rewrite the entire integral in terms of u and du, with no x's left over, or you can't do the substitution", some of them still forget. And I think things would be worse if I regularly did things like substituting du/2x for dx.
Lepton*
Guest

 Posted: Sun Feb 05, 2012 2:44 pm    Post subject: 4 Agree with both. The first approach is the one we use once we know what we're doing, so that's what I teach.
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year by All usersAnonymousdethwingTrojan HorseZag Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum Puzzles and Games----------------Grey Labyrinth PuzzlesVisitor Submitted PuzzlesVisitor GamesMafia Games Miscellaneous----------------Off-TopicVisitor Submitted NewsScience, Art, and CulturePoll Tournaments Administration----------------Grey Labyrinth NewsFeature Requests / Site Problems
You cannot post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum