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Math Help - Fun easy integral

  1. #1
    MHF Contributor Mathstud28's Avatar
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    Fun easy integral

    This is reallyl easy if you see it

    \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\bigg[\int\bigg[\int\bigg[\int{e^{-x^2}dx}\bigg]dx\bigg]dx\bigg]dx
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    This is reallyl easy if you see it

    \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\bigg[\int\bigg[\int\bigg[\int{e^{-x^2}dx}\bigg]dx\bigg]dx\bigg]dx
    Oh and you should put a numerical answer

    Big hint^
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    This is reallyl easy if you see it

    \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\bigg[\int\bigg[\int\bigg[\int{e^{-x^2}dx}\bigg]dx\bigg]dx\bigg]dx
    Come on...no one can do this?
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  4. #4
    MHF Contributor arbolis's Avatar
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    Just a guess

    Well I don't see it but I've done a similar integral once and the answer was 0 due to that the integrated function was odd and the bounds of the integral were opposed in signs. I'd like to "see" what you see... so if it's not too much asked, message me in private so others can do your integral.
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  5. #5
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    Quote Originally Posted by arbolis View Post
    Well I don't see it but I've done a similar integral once and the answer was 0 due to that the integrated function was odd and the bounds of the integral were opposed in signs. I'd like to "see" what you see... so if it's not too much asked, message me in private so others can do your integral.
    I think you got it, I'm fairly sure that Mathstud28 expect some approach using an infinite series. I believe you need to use Taylors theorem to show that e^{-x^2} can be express as a polynomial which only have even powers of x in the series. Then integrating term by term three times yields you with an polynomial with only odd power of x, hence and odd function, so the integral would be zero within those limits.

    also Mathstud28 don't bump your thread constantly, its actually against the site rules.

    Bobak
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by bobak View Post
    I think you got it, I'm fairly sure that Mathstud28 expect some approach using an infinite series. I believe you need to use Taylors theorem to show that e^{-x^2} can be express as a polynomial which only have even powers of x in the series. Then integrating term by term three times yields you with an polynomial with only odd power of x, hence and odd function, so the integral would be zero within those limits.

    also Mathstud28 don't bump your thread constantly, its actually against the site rules.

    Bobak
    Yes you were both correct...I didnt need someone to show the erf(x) I just wanted it known that erf(x) is odd
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  7. #7
    MHF Contributor arbolis's Avatar
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    "I just wanted it known that erf(x) is odd". You succeed with me... Since I almost never studied this function I didn't know that it was odd. Anyway, I believe that it wasn't that easy to see that the integral was equal to 0... If you have never done a similar exercise, then it's quite hard.
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  8. #8
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by arbolis View Post
    "I just wanted it known that erf(x) is odd". You succeed with me... Since I almost never studied this function I didn't know that it was odd. Anyway, I believe that it wasn't that easy to see that the integral was equal to 0... If you have never done a similar exercise, then it's quite hard.
    I dont know...maybe you are right...it seemed obvious to me...but maybe that is because I made it up haha
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  9. #9
    MHF Contributor arbolis's Avatar
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    Nice one, and yes it explains all.
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