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Thread: HSC 2017 MX2 Integration Marathon

  1. #226
    -insert title here- Paradoxica's Avatar
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    Re: HSC 2017 MX2 Integration Marathon

    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.

  2. #227
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    Re: HSC 2017 MX2 Integration Marathon

    We should combine the two integration marathons don't you guys think?

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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Drsoccerball View Post
    We should combine the two integration marathons don't you guys think?
    What's the other integration marathon?
    2016 HSC (Accelerated)
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by pikachu975 View Post
    What's the other integration marathon?
    "Extracurricular Integration Marathon." We might as well since questions are being posted here.

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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Drsoccerball View Post
    "Extracurricular Integration Marathon." We might as well since questions are being posted here.
    No that would be a bad idea as the Extracurricular Integration Marathon deals with integrals at a level well beyond those expected at the MX2 level.

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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post

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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post

    By the reflection property we have

    A quick sketch () lets us deduce that:


    Hence
    Last edited by wu345; 17 Mar 2017 at 6:43 PM.

  8. #233
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    HSC 2017 MX2 Integration Marathon

    Hence, or otherwise, evaluate:



    where n is a positive integer.
    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

    Quote Originally Posted by Paradoxica View Post
    Hence, or otherwise, evaluate:



    where n is a positive integer.

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    Re: HSC 2017 MX2 Integration Marathon

    Using a hyperbolic trigonometric substitution, show that:

  11. #236
    -insert title here- Paradoxica's Avatar
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by wu345 View Post
    FTFY
    Last edited by Paradoxica; 29 Mar 2017 at 11:13 PM.
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    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.

  12. #237
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    Re: HSC 2017 MX2 Integration Marathon

    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.

  13. #238
    Ancient Orator leehuan's Avatar
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post
    Hmm... I wonder where this question came from...
    Paradoxica and wu345 like this.

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    Re: HSC 2017 MX2 Integration Marathon

    Using the fact that

    ,

    Evaluate

    Last edited by wu345; 31 Mar 2017 at 10:50 PM.

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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post
    By the 'remember the answer' method we have

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    Re: HSC 2017 MX2 Integration Marathon

    stuck on this one, any ideas?


  17. #242
    Ancient Orator leehuan's Avatar
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by wu345 View Post
    stuck on this one, any ideas?

    The reverse quotient rule isn't obvious.

    The denominator involves an odd power. Try making it an even power somehow.

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    -insert title here- Paradoxica's Avatar
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by wu345 View Post
    stuck on this one, any ideas?

    RPR
    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

    Quote Originally Posted by wu345 View Post
    stuck on this one, any ideas?







    Last edited by omegadot; 1 Apr 2017 at 10:22 AM. Reason: Typo
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    Re: HSC 2017 MX2 Integration Marathon

    Last edited by stupid_girl; 15 Apr 2017 at 4:57 PM.

  21. #246
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by stupid_girl View Post
    Not only is this unnecessarily obfuscated, it's very difficult for the average MX2 student to comprehend.

    Here's a more legible version of the problem.



    The problem is remarkably trivial, when you come up with the correct substitution.

    I'll leave it to Kingom.
    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.

  22. #247
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post
    Not only is this unnecessarily obfuscated, it's very difficult for the average MX2 student to comprehend.

    Here's a more legible version of the problem.



    The problem is remarkably trivial, when you come up with the correct substitution.

    I'll leave it to Kingom.
    Last edited by Kingom; 15 Apr 2017 at 5:53 PM.

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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post
    Not only is this unnecessarily obfuscated, it's very difficult for the average MX2 student to comprehend.

    Here's a more legible version of the problem.



    The problem is remarkably trivial, when you come up with the correct substitution.

    I'll leave it to Kingom.
    It is purposefully obfuscated but I think average MX2 student should be able to interpret it. End of the day, <f,g>w and <f,g> are just two real numbers. The answer would be the same if I call them star and moon, and ask for star/moon.

    By the way, I think the condition a,b,k being positive cannot be dropped.

  24. #249
    -insert title here- Paradoxica's Avatar
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by stupid_girl View Post
    It is purposefully obfuscated but I think average MX2 student should be able to interpret it. End of the day, w and are just two real numbers. The answer would be the same if I call them star and moon, and ask for star/moon.

    By the way, I think the condition a,b,k being positive cannot be dropped.
    Wrong. k can be strictly less than -1, provided a and b are positive rationals with odd numerator.

    Under the standard real definition of roots.
    Last edited by Paradoxica; 17 Apr 2017 at 4:35 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.

  25. #250
    -insert title here- Paradoxica's Avatar
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    Re: HSC 2017 MX2 Integration Marathon

    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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