Robwalker Posted February 7, 2012 Report Share Posted February 7, 2012 How does ? I can't work it out. Im using the standard integral rule that integral of e^ax dx = (1/a)e^ax Any help is much appreciated. Quote Link to comment Share on other sites More sharing options...
AndrewEH1 Posted February 7, 2012 Report Share Posted February 7, 2012 Where are you stuck? Quote Link to comment Share on other sites More sharing options...
Simpson Posted February 7, 2012 Report Share Posted February 7, 2012 What exactly are you trying to work out? Quote Link to comment Share on other sites More sharing options...
AndrewEH1 Posted February 7, 2012 Report Share Posted February 7, 2012 I'm assuming that he is after a number as the solution. I've solved it, I think... Quote Link to comment Share on other sites More sharing options...
Luke Rainbird Posted February 7, 2012 Report Share Posted February 7, 2012 Excuse the crap picture and writing etc, I've got a f**ked right hand and a stinking cold. For the same reasons it's probably worth checking properly as I'm not exactly thinking clearly today either You've got the product of two functions which you're trying to integrate so you'll be wanting to bust out some integration by parts; I've not been back over it and checked it all makes sense, but even if it's not it should give you a few ideas with a bit of luck. Quote Link to comment Share on other sites More sharing options...
Duncy H Posted February 7, 2012 Report Share Posted February 7, 2012 (edited) Oh god i absolutely hate c3 maths, must have failed it really bad this january so don't believe all i say But basically i do believe that integration by parts should be used. so basically let u=x and therefore du/dx=1 and let dv/dx=e^2x and therefore v=1/2e^2x according to your model The integration by parts formula is as follows... So using that formula... The integration = (x)(1/2e^2x)-1/4e^2x = 1/2xe^2x -1/4e^2x +c (However the +c is not necessary atm) Therefore using the original boundries of 1/2 and 0... =[1/2(1/2)e^2(1/2) -1/4e^2(1/2)] - [1/2(0)e^2(0) -1/4e^2(0)] Now that should hopefully = 1/4 but i have most likely done it wrong Edit: made at least one mistake and corrected it Edit 2: Ahhh beaten to it!! Edited February 7, 2012 by Duncy H Quote Link to comment Share on other sites More sharing options...
ManxTrialSpaz Posted February 7, 2012 Report Share Posted February 7, 2012 (edited) The integral of xe^2x is ((xe^2x)/2) - ((e^2x)/4) (look up integration by parts if unsure how) which simplifies to (e^2x)(x/2 - 1/4). Then with F(0.5) - F(0) you end up with (e^2(0.5))(0.5/2 - 1/4) - (e^2(0))(0/2 - 1/4)) = (e^1)(0) - (1)(-1/4) = (0) - (-1/4) = 1/4 Edit: Knew that would happen. Hope it's all clear now though Edited February 7, 2012 by ManxTrialSpaz Quote Link to comment Share on other sites More sharing options...
Luke Rainbird Posted February 7, 2012 Report Share Posted February 7, 2012 GEEK SNAAAAAAAKE! 8 Quote Link to comment Share on other sites More sharing options...
Robwalker Posted February 7, 2012 Author Report Share Posted February 7, 2012 Spot on guys, i didn't realise it was integration by parts! 1/4 is the correct answer, but i just couldn't see the steps to get there, now i fully understand. Good old TF never lets me down, cheers everyone! Quote Link to comment Share on other sites More sharing options...
MadManMike Posted February 10, 2012 Report Share Posted February 10, 2012 Seriously though, how does anyone understand any of that, at all? Maths has never been my strong point, but that may as well be Japanese written backwards... Quote Link to comment Share on other sites More sharing options...
monkeyseemonkeydo Posted February 10, 2012 Report Share Posted February 10, 2012 Seriously though, how does anyone understand any of that, at all? It's just a process. If you know the process and follow the appropriate rules you can just work through it step by step to get to the answer. Quote Link to comment Share on other sites More sharing options...
Robwalker Posted February 11, 2012 Author Report Share Posted February 11, 2012 88% in the test by the way guys, silly school boy errors let me down. Cheer for the help everyone Quote Link to comment Share on other sites More sharing options...
Jolfa Posted February 12, 2012 Report Share Posted February 12, 2012 I couldn't even begin to make sense of any of the numbers in this thread 1 Quote Link to comment Share on other sites More sharing options...
Robwalker Posted February 28, 2012 Author Report Share Posted February 28, 2012 Thank's to my terrible quality of transposition, i call upon you gurus again. http://uploads.trialsnet.com//monthly_02_2012/post-8224-0-82334500-1330458816_thumb.png How do we get from here, to here: http://uploads.trialsnet.com//monthly_02_2012/post-8224-0-31957900-1330458826_thumb.png Quote Link to comment Share on other sites More sharing options...
Luke Rainbird Posted February 28, 2012 Report Share Posted February 28, 2012 Apologies for another poor phone pic of the page, but; 1 Quote Link to comment Share on other sites More sharing options...
Robwalker Posted February 28, 2012 Author Report Share Posted February 28, 2012 You absolute godsend. It all makes sense when it's in front of me like that. But applying all the rules in the right order and moving things around i just can't keep ontop of. Cheers Luke. TF's resident mathematician Quote Link to comment Share on other sites More sharing options...
MonsieurMonkey Posted February 28, 2012 Report Share Posted February 28, 2012 Stop making me regret doing this shit degree with your maths Rainbird. Quote Link to comment Share on other sites More sharing options...
Luke Rainbird Posted February 28, 2012 Report Share Posted February 28, 2012 Trick is to try and spot which operations are applied to the whole thing and reverse engineer your way out so you get x on it's own Carl; you know where it's at! Quote Link to comment Share on other sites More sharing options...
Robwalker Posted March 13, 2012 Author Report Share Posted March 13, 2012 Can someone check this over for me? I think i've got it... but just want to make sure i'm not missing something out here: If y=4/5(1-e^(-4t)) then multiplying out of brackets y=4/5-4/5e^(-4t) Now to differentiate: as y=e^(ax) dy/dx=ae^(ax) dy/dt=(-4/5)(-4e^(-4t)) dy/dt=3.2e^(-4t) Do you concur? Quote Link to comment Share on other sites More sharing options...
Muel Posted March 13, 2012 Report Share Posted March 13, 2012 Most entertaining thread on TF. I took AS level maths. Dropped it after 3 months, then dropped out of sixth form. I can do geometry stuff easily (cos it's like engineering only simpler), but could never do all the magic shit you lot are drawing up there. Quote Link to comment Share on other sites More sharing options...
Luke Rainbird Posted March 13, 2012 Report Share Posted March 13, 2012 Yeah. Unless things are given elsewhere in decimals I'd probably leave it as 16/5 though to be consistent. While I'm here, if anyone fancies tackling the mountain of coursework I'm going to be buried under for the next month or so it'd much appreciated... 1 Quote Link to comment Share on other sites More sharing options...
Simpson Posted March 13, 2012 Report Share Posted March 13, 2012 Any financial mathematicians fancy having a proof read of my disso before I hand it in? Quote Link to comment Share on other sites More sharing options...
ManxTrialSpaz Posted March 14, 2012 Report Share Posted March 14, 2012 Help please! There's a block fixed to the end of a 2m rod. If the block starts hanging vertically down and then travels through a vertical 0.027m, what would the change in angle be? I kinda know what I should be doing, but can't get my head to work. Quote Link to comment Share on other sites More sharing options...
Luke Rainbird Posted March 14, 2012 Report Share Posted March 14, 2012 <Snip> Edit; Scrub that, give me a sec to make it clearer/right 1 Quote Link to comment Share on other sites More sharing options...
ManxTrialSpaz Posted March 14, 2012 Report Share Posted March 14, 2012 Big thank you Rainbird! You've made all the right assumptions as well. I'm pretty sure I'm pumping out the right answer using theta = cos^-1(1- h/r) Quote Link to comment Share on other sites More sharing options...
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