help with Integration please

• ChoCoChips

  9 Dec 08, 22:31

  

  Hi, I need help with these 4 questions.

  I tried to solve Q1 and 2 myself, but I got stuck.

  For Q1 I took the equation apart,

  which becomes 1/(1+x2) + 2x/(1+x2).

  I can integrate the latter, but not the former.

  But I dont think you can integrate that, can you?

  Which means my method is wrong, but I don't know the correct one. =\

  For Q2,

  I managed to reach a part where I must integrate 2sin2x. [2 (sine x squared)]

  And i got stuck.

  Im totally clueless about Q3 and 4 though. HAHA!

  Please help me!

  Thank you!

   

   

   

• 16/f/lonely

  9 Dec 08, 22:33

  Oh no.....I'm clueless too.

  I used to know....shit.

• charlize

  9 Dec 08, 22:40

  I wish I had the internet to help me with my mathematic problems when I was in secondary school.

• 16/f/lonely

  9 Dec 08, 22:41

  Problem is this is definitely not secondary school stuff.

• maskedangel

  9 Dec 08, 22:44

  thnk god my math paper ended today. . . .
• eagle

  10 Dec 08, 08:44

  sry I can't see the graphics... is there anyway you can rewrite it?

  use this http://www.codecogs.com/components/equationeditor/equationeditor.php

  Get out your equation, select the rendered equation, then paste it here.

• ChoCoChips

  10 Dec 08, 10:29

  Q1.

   

   

  Q2.

  

  er, integration with substitution.

  Q3.

   

  Q4

  If  show that   for  n>= 1

     

  Find I3.

   

  THANK YOU EAGLE LAO DA!

   

   

  edit: the codes not showing up properly..

  maybe u gotta edit/quote my post to see the correct codes.

  that's how i see the eqns.

   

• eagle

  10 Dec 08, 10:49

  as in, select and copy the graphic from there to paste

  do not copy the code

  treat this as MS Word

  or u can copy the code out for me in text.... Then I put in to see

• eagle

  10 Dec 08, 12:56

  Q1)

  

  

  

  

  Note: For , the numerator is a differential of the denominator.

   

   

  Q2)
  and sub

  From ,
  
  

  Sub and

  
  
  
  
  
  

  Since ,

   

  Try to continue here yourself :D

• ChoCoChips

  10 Dec 08, 15:39

  Originally posted by eagle:

  Q1)

  

  

  

  

  Note: For , the numerator is a differential of the denominator.

   

   

  Q2)
  and sub

  From ,
  
  

  Sub and

  
  
  
  
  
  

  Since ,

   

  Try to continue here yourself :D

  
  

  

  eh?!

  how come got this step one?

• maurizio13

  10 Dec 08, 15:47

   

  trigo identity.

   

  sin^2 u = (1 - cos 2u) / 2

   

• ChoCoChips

  10 Dec 08, 16:00

  yea.

  figured it out when i was in the toilet

• wee_ws

  10 Dec 08, 18:02

  Hi,

    For Q3, observe that

  .

    Now the first term is of the standard form . For the second term, complete the square for the expression in the denominator.

    For Q4, it is not assessed in H2 maths.

    Thanks!

  Cheers,
  Wen Shih

• eagle

  10 Dec 08, 18:41

  Thanks a lot for your help wenshih!

  I'm rather busy these few days... Might be even busier till Feb 09... :(

   

  Not sure if TS is taking A levels. From what I know when I went gym, there are poly students who are stuck with integration as well, and Q4 might be part of their syllabus.

• maurizio13

  10 Dec 08, 23:47

  Originally posted by ChoCoChips:

  yea.

  figured it out when i was in the toilet

   

  you should visit the toilet more often.

   

   

• ChoCoChips

  11 Dec 08, 20:26

  thank you sooo much for ur help!

  appreciate that!

  haha

   

  Originally posted by maurizio13:

   

  you should visit the toilet more often.

   

   

  
  yea i should

  maybe i can come up with something that can bag me a nobel prize

• wee_ws

  12 Dec 08, 13:14

  Hi,

    There's no Nobel Prize for mathematics. Fields Medal perhaps :P Jiayou!

  Cheers,
  Wen Shih

• Ahm97sic

  12 Dec 08, 16:04

  Hi Chocochips,

   

  For question 4,

   

  1.  Since there is the part I_n-1 in the RHS of the second formula, we will

  substitute n – 1 into the first formula to get  I_n-1. Use integration by part once on I_n-1.

   

  2.  Next, substitute the answer into the right hand side of the second formula of I_n

   

  3.  Now, use integration by parts twice on I_n in the first formula._.

   

  4.  Next, substitute the answer into the left hand side of the second formula of I_n

   

  5.  Hence, LHS = RHS (Shown)

   

  6.  To get I₃, substitute n = 3 into the first formula of I_n and use integration by part.

   

  Thank you for your kind attention.

   

  Regards,

   

  ahm97sic

   

  PS : As I do not know how to type the mathematical symbols (integral sign, limits etc) in the forum, I can type out the answer using MathType in Microsoft Word 2003 and email you as an attached file.

   

   

• eagle

  12 Dec 08, 17:10

  Hi Ahm97sic,

  you can use this site

  http://www.codecogs.com/components/equationeditor/equationeditor.php

   

  Get your equation out, then copy the graphic by selecting it and then pressing Ctrl C.
  Then paste it here.

  You have to select the graphic for it to work. Right click plus copy won't work.

• Ahm97sic

  13 Dec 08, 00:05

  Hi Eagle,

  Thanks for the information and the useful link.

  Regards,

  ahm97sic

  PS : However, the mathematical symbols appear correct in the edit mode in the homework forum but once the entry is sent. The entry becomes incorrect in the homework forum ie the integral symbol becomes \int.

  I have already typed out the solution to question 4 using Mathtype in Microsoft Word 2003 and it can be sent in an email as an attached file now.