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Homework Help: Integration by expansion

  1. Apr 18, 2014 #1


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    Gold Member

    Consider the integral
    I(x)= \frac{1}{\pi} \int^{\pi}_{0} sin(xsint) dt
    show that
    I(x)= 4+ \frac{2x}{\pi}x +O(x^{3})
    as [itex]x\rightarrow0[/itex].

    => I Have used the expansion of McLaurin series of [itex]I(x)[/itex] but did not work.
    please help me.

    (Note: It is not my homework or coursework question but it is from past exam paper which i am preparing for my exam)
  2. jcsd
  3. Apr 18, 2014 #2

    Simon Bridge

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    Science Advisor
    Homework Helper

    Please show your working.

    Maclearen series: $$f(t)=\sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!}x^n$$

    ##f(t)=\sin(x\sin t),\; f(0)=0##



    etc. until you start getting terms in x3
  4. Apr 19, 2014 #3


    Staff: Mentor

    Physics Forums rules require that you show what you have tried. I sent you a PM about this, and am closing this thread. You are welcome to start a new thread for this problem, but you need to show what you have tried.
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