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Thread: HSC 2017 MX2 Integration Marathon (archive)

  1. #101
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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by InteGrand View Post












    Last edited by InteGrand; 5 Jan 2017 at 9:19 AM.

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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by InteGrand View Post










    Ah yes that makes sense, and so much simpler than my proof. Thank you!
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    Re: HSC 4U Integration Marathon 2017

    This one is a bit tedious.


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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by stupid_girl View Post
    This one is a bit tedious.

    http://imgur.com/a/X7CkW

    EDIT: Yeah I have no idea how to make the LaTeX valid here imgur will have to do haha. Also I'm still learning so if I can improve anywhere just tell me what to do.










    Last edited by calamebe; 23 Jan 2017 at 9:09 PM.
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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by calamebe View Post
    http://imgur.com/a/X7CkW

    EDIT: Yeah I have no idea how to make the LaTeX valid here imgur will have to do haha. Also I'm still learning so if I can improve anywhere just tell me what to do.
    Still learning what? LaTeX, or Integration?

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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by InteGrand View Post
    Still learning what? LaTeX, or Integration?
    LaTeX

    EDIT: Though I guess I can always get better at integration and it doesn't stop at high school
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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by calamebe View Post
    LaTeX
    I guess you can post your LaTeX attempts (or do it in the LaTeX Practice Thread) and people may give LaTeX tips then (since then we can see what's wrong with the code, if anything).
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    Re: HSC 2017 MX2 Integration Marathon

    By considering


    evaluate:

  9. #109
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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by stupid_girl View Post
    This one is a bit tedious.

    I disagree. With the initial substitution , the standard reflection formula may be applied and we obtain the following equivalence after simplification:





    Split and reflect the integral again, but carefully, as follows:



    The value of the integral now simplifies into:

    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  10. #110
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by wu345 View Post
    By considering


    evaluate:
    Using the reflection across the real line with u+x=0, and Glasser's Master Theorem (ceebs showing the intended way but KingOfActing can do that), the integral simplifies completely into:



    This can easily be evaluated in the general form using Differentiation Under The Integral Sign.
    Last edited by Paradoxica; 15 Feb 2017 at 10:29 PM.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: HSC 2017 MX2 Integration Marathon

    Last edited by BenHowe; 22 Feb 2017 at 1:11 PM.
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by BenHowe View Post
    No 2 is easy:

    Last edited by Drongoski; 22 Feb 2017 at 2:15 PM.
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    Re: HSC 2017 MX2 Integration Marathon

    Can't you do two by inspection?

  14. #114
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    Re: HSC 2017 MX2 Integration Marathon

    Reckon q2 is 2u?
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Rathin View Post
    Reckon q2 is 2u?
    Perhaps. That's why I can do this one.
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by si2136 View Post
    Can't you do two by inspection?
    Yes. I did it by inspection but had to show the steps.
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  17. #117
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by BenHowe View Post
    http://m.imgur.com/j3kDVl4

    Q1 answer, it's messy so if you can't understand it or read it then tell me. I don't know if there's a faster method but if there is please tell me.
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  18. #118
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by pikachu975 View Post
    http://m.imgur.com/j3kDVl4

    Q1 answer, it's messy so if you can't understand it or read it then tell me. I don't know if there's a faster method but if there is please tell me.
    Correct! One of those ones where you have to complete the square then do the appropriate trig sub and fiddle with a right angled triangle...
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    Re: HSC 2017 MX2 Integration Marathon

    Are you sure Q3 has closed form solution?
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    Re: HSC 2017 MX2 Integration Marathon

    I don't know what closed form is but you just need to be creative
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    Re: HSC 2017 MX2 Integration Marathon

    For Q4, if you stare at it long enough, you should be able to use reverse quotient rule.

    Let y=1+ln x, then y'=1/x
    The integrand can be written as
    (y-1)/y^2
    =(x'y-xy')/y^2.
    Now, the answer should be obvious.
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by stupid_girl View Post
    For Q4, if you stare at it long enough, you should be able to use reverse quotient rule.

    Let y=1+ln x, then y'=1/x
    The integrand can be written as
    (y-1)/y^2
    =(x'y-xy')/y^2.
    Now, the answer should be obvious.
    Also can work by
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by BenHowe View Post
    4.
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by jathu123 View Post
    4.
    Correct!

    Sorry if this seems like a dumb question, how do you go from line 2-3? Cause I can only do it your way by splitting the integral to . Then if I do the 2nd integral by IBP the remaining integrals cancel, I get the answer.
    Last edited by BenHowe; 24 Feb 2017 at 11:16 AM.
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  25. #125
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by BenHowe View Post
    Sorry if this seems like a dumb question, how do you go from line 2-3?
    My bad, should have wrote it there. I just used reverse quotient rule, with the denominator being 1+lnx and the numerator x


    Ohhh just realized stupid_girl already done this above
    Last edited by jathu123; 24 Feb 2017 at 11:16 AM.
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