calculus question is there a typo here,
number 2, where it says then dz = f(z) du, shouldn't it say, then du = f(z) dz
No, it's not a typo.
that doesnt make sense
if u = sin z , right? then du = cos z dz ,
Right. And dz =?
dz = 1/ cos z du ?
yes
why would they ask that , that seems strange
Not really, that's how I solve all my u-subs.
hmmm
thats redundant
Suit yourself. ;p
one sec, let me check
where exactly are you doing u substitution then
u = sin z , then du = cos z dz , so if dz = du/ cos z we have integral du/ u^4, oh the cos z cancels/
you might as well just substitute it directly
so you get integral du / u^4
this saves the step of having to plug that dz back in and then cancel, the whole point of u substitution i thought was to change the variables
\[u = sin\ z \implies du = (cos\ z)dz \implies dz = \frac{1}{cos\ z} du\] \[\implies \int \frac{cos\ z}{sin^4z}dz = \int \frac{cos\ z}{u^4}(\frac{1}{cos\ z})du\] \[ = \int \frac{1}{u^4} du \]
Sometimes it works nicely, othertimes you have to do a bit of finagling.
I'm not sure what you mean by redundancy.
its redundant, you can skip that step , ok because du = cos z dz, and you already have cos z dz in the numerator
Sure, but sometimes it's not that obvious.
what do you mean
i NEVER use this approach
I always do.
give me problem and i will show yuo my approach
I understand the other way, but too often it's just a matter of doing something in your head and I prefer to have it spelled out explicitly.
hmmm, it seems odd , i guess i learned it a different way
everyone's brains work a little differently =)
well let me show you what i do, and you compare it with what you do
give me a problem, lets see
integral x e^(x^2) dx
u = x^2 , du = 2x dx , du/2 = x dx (its ok to divide out constant) so integral e^u du / 2
sure, fine.
ok :)
http://www.youtube.com/watch?v=Cj4y0EUlU-Y About different ways people think.
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