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Thread: HSC 2017 MX2 Integration Marathon (archive)

  1. #251
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post



    though in reality these questions are trivial and can easily be done by inspection
    Last edited by Kingom; 13 May 2017 at 11:15 PM.

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    Re: HSC 2017 MX2 Integration Marathon

    If b>a>0 evaluate:

    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
    If b>a>0 evaluate:

    Trivial by inspection


    Note the potential tautology if ab=-1 cannot occur as b>a>0.
    Last edited by Kingom; 21 Jun 2017 at 11:26 PM.
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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by Paradoxica View Post




    Simplifying the derivative in Mathematica confirms the result.
    Hey, sorry for being so bad at this subject, but how do you know to use that substitution? Thinking process? What are some key things to look out for when attempting a question?
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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by EngineeringHelp View Post
    Hey, sorry for being so bad at this subject, but how do you know to use that substitution? Thinking process? What are some key things to look out for when attempting a question?
    Eliminate irrational functions using whatever you have at your disposal.

    The only three ways of doing so are:

    Classical Trigonometric Substitution (High School level)

    Hyperbolic Trigonometric Substitution (University level)

    Euler Substitution (Extracurricular)
    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 4U Integration Marathon 2017

    Quote Originally Posted by Paradoxica View Post
    Eliminate irrational functions using whatever you have at your disposal.

    The only three ways of doing so are:

    Classical Trigonometric Substitution (High School level)

    Hyperbolic Trigonometric Substitution (University level)

    Euler Substitution (Extracurricular)
    Ooh, so for the HSC all i should worry about is a Trig Sub? As it wouldn't be right to be asked questions requiring the other two, right?
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    Re: HSC 4U Integration Marathon 2017

    Also, does anyone have any 'not so complicated' reduction-formula questions? If so, please post. Im assuming Paradoxica will be supplying solutions xD <3
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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by EngineeringHelp View Post
    Also, does anyone have any 'not so complicated' reduction-formula questions? If so, please post. Im assuming Paradoxica will be supplying solutions xD <3
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    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by pikachu975 View Post
    ...ew
    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 4U Integration Marathon 2017

    Quote Originally Posted by pikachu975 View Post
    Lmao use Mathematical Induction to prove? Stuff In

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    Re: HSC 2017 MX2 Integration Marathon

    Last edited by leehuan; 27 Jun 2017 at 11:07 AM.
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    Re: HSC 2017 MX2 Integration Marathon

    Try this one.

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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by stupid_girl View Post
    Try this one.
    d(lnsqrt(sin3x)) = 3/2 * cot3x * dx
    2/3 * d(lnsqrt(sin3x)) = cot3x dx

    Therefore integrand becomes 2/3 * sec^2 (lnsqrt(sin3x)) * d(lnsqrt(sin3x))
    Integrate:
    = 2/3 * tan(lnsqrt(sin3x)) + C
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by pikachu975 View Post
    d(lnsqrt(sin3x)) = 3/2 * cot3x * dx
    2/3 * d(lnsqrt(sin3x)) = cot3x dx

    Therefore integrand becomes 2/3 * sec^2 (lnsqrt(sin3x)) * d(lnsqrt(sin3x))
    Integrate:
    = 2/3 * tan(lnsqrt(sin3x)) + C
    Not bad.
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    Re: HSC 2017 MX2 Integration Marathon

    long time no integrals
    here's a couple of good ones to try out!

    Last edited by jathu123; 12 Aug 2017 at 5:16 PM. Reason: fixed typo
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by jathu123 View Post
    long time no integrals
    here's a couple of good ones to try out!





    Last edited by pikachu975; 12 Aug 2017 at 11:13 PM.
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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by jathu123 View Post
    long time no integrals
    here's a couple of good ones to try out!










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    Re: HSC 2017 MX2 Integration Marathon

    Quote Originally Posted by jathu123 View Post
    long time no integrals
    here's a couple of good ones to try out!












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    Re: HSC 2017 MX2 Integration Marathon

    Integrate 1/[(sinx)sqrt(sin2x)]
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  20. #270
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    Re: HSC 2017 MX2 Integration Marathon

    2017 thread is now closed.
    The new 2018 marathon has been created.

    dan
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