Integration qn

• eagle

  27 Oct 07, 22:34

  Originally posted by tanjun:

  lol. The by parts method is really unexpected. It is the so called true power of the by parts.
  
  
  
  Try this question. Very interesting too. Have to use tamago method to solve it.

  i forgot how already, but I think if you use complex numbers, you can solve it too........ you do the by parts, I do the complex numbers, then compare answer?
  
  edit: I used complex numbers (euler's formula) to solve, my final answer is
  
  1/2 e^x (cos x + sin x)
  
  Differentiating it gives you the answer above, so I'm pretty sure it is correct. I shall now type it out on MS word, and post a screenshot of it here
• ^tamago^

  27 Oct 07, 22:44

  Originally posted by eagle:

  Differentiating it gives you the answer above, so I'm pretty sure it is correct. I shall now type it out on MS word, and post a screenshot of it here

  thanks in advance, eagle.
• HyuugaNeji

  27 Oct 07, 22:48

  recursive formula ba... cos integrate or differentiate e^x always e^x.
  
  so just take
  INT e^x(cos x) =e^x(cos x) - INT e^x(-sin x)
  =e^x(cos x) + INT e^x(sin x)
  =e^x(cos x) + e^x(sin x) - INT e^x(cos x)
  
  so 2 INT e^x (cos x) = e^x(cos x + sin x). then divide by 2.
  
• eagle

  27 Oct 07, 22:50

  Originally posted by HyuugaNeji:

  recursive formula ba... cos integrate or differentiate e^x always e^x.
  
  so just take
  INT e^x(cos x) =e^x(cos x) - INT e^x(-sin x)
  =e^x(cos x) + INT e^x(sin x)
  =e^x(cos x) + e^x(sin x) - INT e^x(cos x)
  
  so 2 INT e^x (cos x) = e^x(cos x + sin x). then divide by 2.
  

  Yep, this is another way
  And it should be the way to do for A levels
  
  Anyway, for those who want to see the complex number way, here it is:
  
  
• teraexa

  27 Oct 07, 22:55

  Originally posted by tanjun:

  lol. The by parts method is really unexpected.
  
  
  
  Try this question. Very interesting too. Have to use tamago method to solve it.

  This question or something similar came out for the ACJC prelims.
• tanjun

  27 Oct 07, 22:57

  
  
  My teacher mentioned about this trick last time of by parts to solve this type of questions. And my ans is the same as yours.
• HyuugaNeji

  27 Oct 07, 23:04

  what program do you people use to get the integration symbol?
• eagle

  27 Oct 07, 23:06

  Originally posted by HyuugaNeji:

  what program do you people use to get the integration function?

  I used MS Word
• HyuugaNeji

  27 Oct 07, 23:16

  Originally posted by eagle:

  I used MS Word

  wow...k
• tanjun

  27 Oct 07, 23:17

  Originally posted by HyuugaNeji:

  what program do you people use to get the integration symbol?

  MS word too. You can go to help and type integration as the helping word. If the application supports mathematical function, they will display a list of instructions to help you with them.
• ^tamago^

  27 Oct 07, 23:17

  tanjun can try disabling spelling checks.