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Math Help - I think I made a mistake somewhere

  1. #1
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    I think I made a mistake somewhere

    The question states to prove beta= sqrt(pi ln 5) whereas I get beta= pi ln 5. I attached my steps below

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  2. #2
    MHF Contributor
    Opalg's Avatar
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    You have mishandled the limits of integration when making the substitution in the integral. If t=\theta^2 then t=0 when \theta=0, and t=\beta^2 when \theta=\beta. So the integral should become \displaystyle\int_0^{\beta^2}\!\!\!\tfrac12\sqrt t e^{2t/x}\tfrac1{2\sqrt t}}\,dt.

    You have worked out the integral correctly (apart from having \sqrt t instead of \beta^2 as the upper limit of integration), and it leads to the result 5 = e^{\beta^2/\pi}, which is what you want.
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