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Math Help - Integration by expansion

  1. #1
    Junior Member
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    Integration by expansion

    Consider the integral
    \begin{equation}
    I(x)= \frac{1}{\pi} \int^{\pi}_{0} sin(xsint) dt
    \end{equation}
    show that
    \begin{equation}
    I(x)= 4+ \frac{2x}{\pi}x +O(x^{3})
    \end{equation}
    as $x\rightarrow0$.
    => I Have used the expansion of McLaurin series of $I(x)$ but did not work.
    please help me.
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  2. #2
    MHF Contributor
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    Re: Integration by expansion

    I'm not getting that 4. I'm getting only $\dfrac {2x}{\pi}$
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  3. #3
    Senior Member
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    Re: Integration by expansion

    4 will not come only 2x/pi will come check wolfram alpha
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