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Math Help - Puzzling Ans

  1. #1
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    Puzzling Ans

    Hi all, Below are 2 solutions which are very puzzling. Can anyone explain this?
    Thanks alot.

    Puzzling Ans-q1solution.jpg

    For this question? How did step one when integrating from -1 to 1 jumped to step 2 integrating from 0 to 1? and pi become 2pi instead?

    Puzzling Ans-q2solution.jpg

    For this question, isnt the answer suppose to be e^1 instead of e^2? since at the last step, when xe^-2x tends to infinity, its suppose to be 1 right?

    Experts, what are your opinion?
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  2. #2
    MHF Contributor

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    Re: Puzzling Ans

    If f is an integrable even function then

    \int_{ - a}^a {f(x)dx}  = 2\int_0^a {f(x)dx} ~.
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