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Thread: I could not solve this integral

  1. #1
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    I could not solve this integral

    hello every body
    i wondering if any one can help me with this integral
    I could not solve this integral-capture.png
    thank you
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  2. #2
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    Re: I could not solve this integral

    Assuming $a \neq 0$, rewrite it as

    $\begin{align*}
    \displaystyle S &= \sum \limits_{k=0}^\infty~\left(\int_{\frac{k \pi}{a}}^{\frac{(k+1)\pi}{a}}~(-1)^k e^{-\beta x}\sin(a x)~dx\right) \\ \\

    &=\sum \limits_{k=0}^\infty~(-1)^k\left(\int_{\frac{k \pi}{a}}^{\frac{(k+1)\pi}{a}}~e^{-\beta x}\sin(a x)~dx\right)\\ \\

    &=\sum \limits_{k=0}^\infty~(-1)^k \left(\dfrac{\left(e^{\frac{\pi \beta }{a}}+1\right) e^{-\frac{\pi \beta (k+1)}{a}} (a \cos (\pi k)+\beta \sin (\pi k))}{a^2+\beta ^2}\right) \\ \\

    &= \dfrac{a \left(e^{\frac{\pi \beta }{a}}+1\right)}{\left(e^{\frac{\pi \beta }{a}}-1\right) \left(a^2+\beta ^2\right)}

    \end{align*}$
    Thanks from nicekiller231
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  3. #3
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    Re: I could not solve this integral

    thank you so much for your help!!
    I have been following the same path to solve it. and I asking if there are no a negative signe missed since the 3 ligne
    I could not solve this integral-captures.png
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  4. #4
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    Re: I could not solve this integral

    Quote Originally Posted by nicekiller231 View Post
    and I asking if there are no a negative signe missed since the 3 ligne
    I don't understand what you are saying.
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