Indefinite integral

  • Thread starter ProBasket
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  • #1
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[tex]\int sin(9x)sin(16x)dx[/tex]

is there another way of solving the problem above besides using the multiple angles formula?
 

Answers and Replies

  • #2
609
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use this identity:

[tex]
sin u = \frac{e^{iu}-e^{-iu}}{2i}
[/tex]

edit:
expand the sine in term of exponential, multiply them and regroup them into 2 cosine, then do the integral
 
Last edited:
  • #3
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wow looks more difficult than using multiple angles formula. i just thought there's an easier way to do it so i wont have to remeber crazy amount of formulas when it's test day.
 
  • #4
ehild
Homework Helper
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ProBasket said:
[tex]\int sin(9x)sin(16x)dx[/tex]

is there another way of solving the problem above besides using the multiple angles formula?
use

[tex] \sin{\alpha}\sin{\beta} = \frac{\cos(\alpha-\beta) - \cos(\alpha + \beta)}{2}[/tex]

ehild
 
  • #5
609
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actually, my way is much much much more easier than remember you formulas.....
I can eye ball the answer using my way......
the answer is....
1/14 sin7x - 1/50 sin25x
the expansion of the complex number is easy.... there are only 4 terms
 

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