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Thread: HSC 2018 MX2 Integration Marathon

  1. #1
    Taking a break! dan964's Avatar
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    HSC 2018 MX2 Integration Marathon

    Integration marathon for MX2 2018
    Post integration questions within scope of MX2

    First question: (from pikachu975)
    Integrate 1/[(sinx)sqrt(sin2x)]

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    -insert title here- Paradoxica's Avatar
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by pikachu975
    Hint: expand and substitute
    Last edited by Paradoxica; 10 Oct 2017 at 6:47 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 2018 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post
    Hint: expand and substitute
    Further hint: take something out of the root and simplify, then substitute

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    Re: HSC 2018 MX2 Integration Marathon

    Wait the sinx is on the denominator. It's basically the BOS trial question
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by pikachu975 View Post
    Wait the sinx is on the denominator. It's basically the BOS trial question
    Yup. FYI the mistranscribed integral is equivalent to 1/root(2) integral of root(tanx) which has been calculated to exhaustion.
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by Kingom View Post
    Yup. FYI the mistranscribed integral is equivalent to 1/√2 integral of √tanx which has been calculated to exhaustion.


    The rest is trivial.
    Kingom and pikachu975 like this.
    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 2018 MX2 Integration Marathon


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    Re: HSC 2018 MX2 Integration Marathon

    For , define .
    (a)Show that f(x) is decreasing. Write down the maximum value of f(x).
    (b)Find .

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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by omegadot View Post


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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by stupid_girl View Post
    For , define .
    (a)Show that f(x) is decreasing. Write down the maximum value of f(x).
    (b)Find .







    _________________________________________



    Last edited by leehuan; 6 Nov 2017 at 11:24 PM.
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    Re: HSC 2018 MX2 Integration Marathon


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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by leehuan View Post
    same
    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 2018 MX2 Integration Marathon

    Quote Originally Posted by leehuan View Post




















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    Re: HSC 2018 MX2 Integration Marathon




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    Re: HSC 2018 MX2 Integration Marathon



    Also spoiler for the one above:
    Spoiler (rollover to view):
    Do the same substitution as the one above it

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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by leehuan View Post


    Also spoiler for the one above:
    Spoiler (rollover to view):
    Do the same substitution as the one above it
    I don't think



    is the right substitution for that.
    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 2018 MX2 Integration Marathon

    This one is fairly straight-forward.

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    Re: HSC 2018 MX2 Integration Marathon

    A nice one
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by jathu123 View Post
    A nice one
    sik MIT steal
    leehuan likes this.
    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.

  20. #20
    Ancient Orator leehuan's Avatar
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post
    sik MIT steal
    That being said is there a way of doing it using only 4U methods
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  21. #21
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by leehuan View Post
    That being said is there a way of doing it using only 4U methods
    not without assuming the standard series expansion of e
    leehuan likes this.
    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. #22
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post
    not without assuming the standard series expansion of e
    Which isn't even 4U.

    Savage,

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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by leehuan View Post
    Which isn't even 4U.

    Savage,
    We can prove series expansion of $e$ using 4U maths.
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  24. #24
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by sharky564 View Post
    We can prove series expansion of $e$ using 4U maths.
    using a highly unmotivated proof, sure.... xd
    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. #25
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    Re: HSC 2018 MX2 Integration Marathon

    but in the hsc such a question would not be likely to appear, all that work just for a simple integral....
    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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