#apache #archlinux #asterisk #centos #debian #gentoo #haskell #kde #kubuntu #lisp #math #mysql #perl #python #ruby-lang #rubyonrails #suse #ubuntu #vim #wikipedia 0 1 2 3 4 5 6 7 8 9 10 11 12
Top Prev 5406 5407 5408 5409 5410 5411 5412 5413 5414 5415 5416 5417 5418 5419 5420 5421 5422 5423 5424 Next
#math
<lokieee> i'm an engineer and i just asked a question about scienfic notation, so don't feel bad
<asphyxia> adamjon858: Exactly
<adamjon858> heh
<dn4> asphyxia I don't follow you there
<adamjon858> are any of you familiar with the uv - $vdu
<dn4> asphyxia my book is showing me a geometric proof for why sin(x)/(x)=1
<cyclicFifths> yes, but i think asphyxia's notation is actually more revealing
<dn4> asphyxia I'll study some more
<adamjon858> not as in are you familiar with integration by parts, but more so are you familiar with setting it up as uv/vdu other than F(x) G(x)
<adamjon858> Because using u,du,dv,v I usually get mixed up on what i should use for u and dv
<asphyxia> dn4: Just familiarize your self with L'Hopital (or is it L'Hospital?)
<GWild_Gen2> lol
<adamjon858> does it really matter?
<Dacicus> asphyxia: It's both.
<asphyxia> Dacicus: hmm... weird.
<adamjon858> if i have $4x x^2 dx and i decide to use integration by parts can i use u=x^2, dv=4x dx or u=4x dx, dv = x^2 and come out to the same problem either way?
<asphyxia> dn4: but remember that one for later - it is very common tool in calculus of one variables.
<cyclicFifths> adamjon858: it wouldn't hurt to try both, it's more work, but you will understand after you do several problems why you are choosing the function better
<adamjon858> Also, how do I know if I should use normal integration, integration by substitution, integration by parts, tabular integratoin, or euler's method
<asphyxia> dn4: There are actually some twists - you can for example try l'Hopital on infinity/infinity too, i.e. a fraction of functions where both numerator and denominator goes to infinity as the approach the same input value.
<adamjon858> cyclicFifths: so it does matter which one I pick?
<cyclicFifths> adamjon858 : these things come with experience.
<asphyxia> adamjon858: Mostly you guess. If it involves exponential or trigonometric functions and polynomials, a good guess is often int by parts
<cyclicFifths> adamjon858: yes, it does matter... you have to think: you are trying to make a complicated integral less complicated
<adamjon858> cyclicFifths: ok I thought so
<cyclicFifths> adamjon858: try something like: Integral[ x^2*sin(x) ]
<adamjon858> What happens if use integration by parts or something on a normal problem? Should it still work out
<adamjon858> cyclicFifths: Wouldn't I use integration for parts for that?
<cyclicFifths> see what happens if you let u = x^2, then see what happens when you let x^2 = sin(x)... then ask yourself why one of them worked
<adamjon858> cyclicFifths: And wouldn't tabular integration be best?
<cyclicFifths> sry, that second x^2 should be u
<cyclicFifths> tabular?
<Steve|Office> Tabular integration would be looking it up in a table?
<adamjon858> yeh.
<adamjon858> no
<cyclicFifths> i don't think i understand
<adamjon858> http://marauder.millersville.edu/~bikenaga/calc/parts/partspf.html
<asphyxia> adamjon858: The notation that has always worked for me, when integrating by parts is $ f(x)g(x)dx = F(x)g(x) - $F(x)g'(x)dx - then you dont mix the infinitesimals up (dv, du, dx, you know)
<adamjon858> basically with problems like that where one of the variables degenerates into 0 and the other one remains relatively the same
<adamjon858> asphyxia: but than what do you use for f(x) and g(x)
<adamjon858> You wouldn't do it in order would you?
<asphyxia> well, no, else you could just rearrange for proper use
<adamjon858> if you had tan(lnx) dx what would you put for f(x) and what for g(x)
<asphyxia> $ x^4 lnx dx = $ lnx x^4 dx
<adamjon858> so it really is not much different than what i had..other than u's look a lot like v's
<asphyxia> adamjon858: If I had that, I would integrate by substitution.
<asphyxia> As tan(lnx) is a composition.
<cyclicFifths> adamjon858: it's the exact same as the u v notation
<asphyxia> or I would try, I havent tried yet.
<adamjon858> So if I have only one x and i can't do it normally I should goto substitution
Previous Page Next Page