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Math Help - integral with nice result

  1. #1
    Eater of Worlds
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    integral with nice result

    If anyone wishes to tackle it, go ahead and integrate and see what a cool result you get. I thought it was anyway.

    \int_{0}^{1}\frac{x^{4}(1-x)^{4}}{1+x^{2}}dx

    It shouldn't be too bad. Some division and term by term integration.
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    Quote Originally Posted by galactus View Post
    If anyone wishes to tackle it, go ahead and integrate and see what a cool result you get. I thought it was anyway.

    \int_{0}^{1}\frac{x^{4}(1-x)^{4}}{1+x^{2}}dx

    It shouldn't be too bad. Some division and term by term integration.
    Putnam problem.

    The result is,
    \frac{22}{7} - \pi

    I seen this like 5 times already.
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  3. #3
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    OK, sorry, I didn't know. I didn't realize it was a Putnam problem. Rather cliche then.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by galactus View Post
    OK, sorry, I didn't know. I didn't realize it was a Putnam problem. Rather cliche then.
    yes. in fact, it was mentioned on this forum already, see page 2 here. it was used to prove that 22/7 exceeds pi

    but thanks for reminding me about that impressive result. i dont get to see it as often as TPH does
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    Read about it here.

    Here is a much more nastier one I found on AoPs:
    \frac{355}{113}-\pi = \int_0^1\frac{(25+816x^2)[x(1-x)]^8}{3164(1+x^2)} dx
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  6. #6
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    I seen it in "Gamma, exploring Euler's constant" by Julian Havil.

    A nice book.
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  7. #7
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    Quote Originally Posted by galactus View Post
    I seen it in "Gamma, exploring Euler's constant" by Julian Havil.
    I really want that book! But I cannot buy it since I am reading math textbooks, I do not have time. It makes me angry that I cannot do everything at the same time!
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