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Sine integral

  1. Mar 6, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]S_N (x) = \frac{2}{\pi} \int_0^x \frac{\sin (2 N t )}{\sin (t)} \; d{t}[/tex]

    use suitable small angle formula to show


    [tex]S_N \Big( \frac{\pi}{2 N} \Big) = \frac{2}{\pi} \int_0^{\pi} \frac{\sin u}{u} d{u}[/tex]

    2. Relevant equations

    i guess the suitable small angle formula is

    [tex] \sin (\theta) \sim \theta [/tex]

    when [tex] (\theta) [/tex] is small...

    3. The attempt at a solution


    i have tried to do some substations but just cant get both numerator and denominator to the right thing


    any sugguestions will be appreciated

    Thank YOU
     
  2. jcsd
  3. Mar 6, 2009 #2

    lurflurf

    User Avatar
    Homework Helper

    change variable
    u=2N*t
    then
    sin(small)~small
     
  4. Mar 6, 2009 #3
    It looks like you already know they want you to assume [tex]$\sin(t)=t$[/tex]. Your next step is to find an appropriate "u substitution." Try [tex]$ u = 2Nt$[/tex] so that you have [tex]$ \int_0^{\pi/2N} \frac{\sin{(2Nt)}dt}{t} = \int_{0}^{?} \frac{\sin{u}}{u}du$[/tex]. Use algebra to find [tex]$ ? $[/tex] and [tex] $ du $ [/tex].
     
    Last edited: Mar 6, 2009
  5. Mar 7, 2009 #4
    Hi there
    I have tried this already (actually 7 days ago)
    still using
    [tex] u = 2 N t [/tex] i can get the correct limits but
    i just can't justify that the bottom
    [tex] t [/tex] just goes to [tex] u [/tex]
    how do i jusitfy that?

    Thank you

    ++++++++++++++++++++++++++++
    holly!!!!!!!!!!!!!!!!!!!!!!

    I got it
    right after the click "post quick reply".....

    THANK YOU ALL

    :P
     
  6. Mar 7, 2009 #5
    [tex]\frac{du}{u} = \frac{2Ndt}{2Nt} = \frac{dt}{t}[/tex]
     
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