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Thread: Integral from negative infinity to positive infinity?

  1. #1 Integral from negative infinity to positive infinity? 
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    Is this correct?




    Thanks in advance!


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  3. #2  
    Moderator Moderator AlexP's Avatar
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    It does not equal infinity. But if you meant that it diverges, then yes, it does.


    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
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  4. #3  
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    I would think it is undefined? My teacher said it is equal to infinity because 5x approaches to positive infinity faster than x approaches to negative infinity and I did not agree because it comes out to be infinity minus infinity.
    If it is not undefined, what is it? If it is undefined, how could I better express to my teacher that they're incorrect?
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  5. #4 Re: Integral from negative infinity to positive infinity? 
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    Quote Originally Posted by m84uily
    Is this correct?




    Thanks in advance!
    Integrals can be broken into pieces, so:



    If then you can reduce that to , which obviously diverges.

    (Edit: Sorry, forgot to divide by 2.)
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  6. #5 Re: Integral from negative infinity to positive infinity? 
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    Quote Originally Posted by MagiMaster
    Integrals can be broken into pieces, so:



    If then you can reduce that to , which obviously diverges.














    Which is undefined? Maybe I'm misunderstanding the word "divergent" I take it to mean that the sums do not approach some limit. If that's right then I understand its being divergent, I just want to know if my teacher's reasoning is incorrect or not.
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  7. #6  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Your teacher isn't exactly wrong, just not exactly accurate. It'd be more proper to say that:


    Infinities generally don't make much sense outside of limits, so without being more precise, it'd be hard to say for sure what's right or wrong.
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  8. #7  
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    Quote Originally Posted by MagiMaster
    Your teacher isn't exactly wrong, just not exactly accurate. It'd be more proper to say that:


    Infinities generally don't make much sense outside of limits, so without being more precise, it'd be hard to say for sure what's right or wrong.
    Okay! Thanks :-D
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  9. #8  
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    I believe all parties here, including your teacher, do not understand the meaning of the phrase

    .

    What this means is that



    as and independently of each other. It is not sufficient to set a = -b and take the limit.

    In this particular example, the integral is undefined.
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  10. #9  
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    Quote Originally Posted by m84uily
    I would think it is undefined? My teacher said it is equal to infinity because 5x approaches to positive infinity faster than x approaches to negative infinity and I did not agree because it comes out to be infinity minus infinity.
    If it is not undefined, what is it? If it is undefined, how could I better express to my teacher that they're incorrect?
    salsaonline, unsurprisingly, is correct.

    So are you.

    Are you taking a high-school calculus class ? If so, there is probably little that you can do to convince your teacher. If not, find a better college.

    You will see such questions treated properly, and in some depth, in a university class on real analysis. If the integrand is non-negative, things are fairly simple. If not, the issues can be subtle.
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  11. #10  
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by m84uily
    I would think it is undefined? My teacher said it is equal to infinity because 5x approaches to positive infinity faster than x approaches to negative infinity and I did not agree because it comes out to be infinity minus infinity.
    If it is not undefined, what is it? If it is undefined, how could I better express to my teacher that they're incorrect?
    salsaonline, unsurprisingly, is correct.

    So are you.

    Are you taking a high-school calculus class ? If so, there is probably little that you can do to convince your teacher. If not, find a better college.

    You will see such questions treated properly, and in some depth, in a university class on real analysis. If the integrand is non-negative, things are fairly simple. If not, the issues can be subtle.
    Yeah, I'm in high school, I guess I'll give up on trying to convince my teacher and just do things their way for marks. I'll be looking forward to that class on real analysis :-D
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