Page 1 of 11 123 ... LastLast
Results 1 to 25 of 251
Like Tree52Likes

Thread: HSC 2017 MX2 Integration Marathon

  1. #1
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,676
    Rep Power
    6

    HSC 2017 MX2 Integration Marathon

    Post integrals here to help/test the Extension 2 students of 2017

    Here is a decent question to begin



    Note that there are still unanswered questions in the 2016 marathon that you may like to consider.

  2. #2
    Member
    Join Date
    Apr 2015
    HSC
    2017
    Gender
    Male
    Location
    Sydney
    Posts
    256
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017

    Lol i think this method is a complete unintended tedious one
    use the substitution x=sqrt(3)sin(theta). the new limits are now 0 to sin^-1(1/sqrt(3)). and dx=sqrt(3)cos(theta). Sub it in, the integrand becomes 9sin^2(theta)cos^2(theta). Which can be written as 9/4(sin2theta)^2. Using the double angle cos formula, it will turn out to be 9/8(1-cos(4theta)). Now integrating it, it becomes 9/8(theta-(sin4theta)/4)) from 0 to sin^-1(1/sqrt3). Expanding out the sin4theta (either by continuous use of double angle formula or DMT) and subbing in the limits will give a final answer of 1/8(9arcsin(1/sqrt3)-sqrt2).

    soz for no latex might add it when im free
    Last edited by jathu123; 18 Oct 2016 at 7:36 PM.
    2017 HSC

    Maths Ext 2 ~ Maths Ext 1~ Physics ~ Chemistry ~ English Advanced

    >97 pls

  3. #3
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,772
    Rep Power
    5

    Re: HSC 4U Integration Marathon 2017

    leehuan likes this.

  4. #4
    Hi Φ Rathin's Avatar
    Join Date
    Mar 2015
    HSC
    2017
    Gender
    Male
    Posts
    2,672
    Rep Power
    3

    Re: HSC 4U Integration Marathon 2017

    It will be a while before I attempt in this marathon...
    2016 Preliminary

    Maths Extension • English Advanced • Biology • Legal Studies • Physics • PDHPE

    2017 HSC

    Maths Extension 2 • English Advanced • Biology • Physics • PDHPE

    Atar aim: 97
    Desired Course: Physiotherapy

  5. #5
    -insert title here- Paradoxica's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Location
    Outside reality
    Posts
    2,362
    Rep Power
    4

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by InteGrand View Post
    ...

    This isn't funny anymore.
    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.

  6. #6
    -insert title here- Paradoxica's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Location
    Outside reality
    Posts
    2,362
    Rep Power
    4

    Re: HSC 4U Integration Marathon 2017

    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.

  7. #7
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,772
    Rep Power
    5

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by Paradoxica View Post
    ...

    This isn't funny anymore.
    Worth exposing 2017'ers to since they may not have followed the older Marathons. (Wasn't intended as a joke integral.)
    Last edited by InteGrand; 18 Oct 2016 at 8:16 PM. Reason: Typo

  8. #8
    Cadet
    Join Date
    Apr 2015
    HSC
    2019
    Gender
    Male
    Posts
    33
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017

    Quick question with regards to integrals. are we allowed to integrate by inspection in the hsc. thanks

  9. #9
    Loquacious One Drsoccerball's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Undisclosed
    Posts
    3,668
    Rep Power
    5

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by Kingom View Post
    Quick question with regards to integrals. are we allowed to integrate by inspection in the hsc. thanks
    If the integrals easy enough to inspect such as a reverse product rule then you can... You can't just do what Paradoxica does and just say for question 16 integral "by inspection...".

  10. #10
    Loquacious One Drsoccerball's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Undisclosed
    Posts
    3,668
    Rep Power
    5

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by Paradoxica View Post
    Chose otherwise soz. I can see the borders way but why bother...

  11. #11
    Cadet
    Join Date
    Apr 2015
    HSC
    2019
    Gender
    Male
    Posts
    33
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017


  12. #12
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,772
    Rep Power
    5

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by Drsoccerball View Post
    Chose otherwise soz. I can see the borders why but why bother...
    I guess he considered that 'masochistic'? (Not really sure how it is, but anyway.)

    Anyway, just note that by point symmetry, the area under the curve (and hence the integral) is half the area of the rectangle enclosing the arc in question, i.e. 1/2 * (pi/2) = pi/4.
    Last edited by InteGrand; 19 Oct 2016 at 4:38 AM. Reason: Typo

  13. #13
    Cadet
    Join Date
    Apr 2015
    HSC
    2019
    Gender
    Male
    Posts
    33
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by Drsoccerball View Post
    If the integrals easy enough to inspect such as a reverse product rule then you can... You can't just do what Paradoxica does and just say for question 16 integral "by inspection...".
    aww no using inspection in everything you integrate. thanks anyway drsoccerball

  14. #14
    -insert title here- Paradoxica's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Location
    Outside reality
    Posts
    2,362
    Rep Power
    4

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by Drsoccerball View Post
    Chose otherwise soz. I can see the borders way but why bother...
    Too long. One can observe:



    Then use the fact 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.

  15. #15
    Junior Member
    Join Date
    Apr 2016
    HSC
    2017
    Gender
    Undisclosed
    Posts
    172
    Rep Power
    1

    Re: HSC 4U Integration Marathon 2017

    At school has anyone started 4 unit integration? Because at my school we don't start it till next year term 2
    Mathematics Extension 2 - Physics - Chemistry - Economics - English Advanced

  16. #16
    Executive Member
    Join Date
    Jul 2014
    HSC
    2017
    Gender
    Female
    Location
    SYD
    Posts
    1,489
    Rep Power
    3

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by frog1944 View Post
    At school has anyone started 4 unit integration? Because at my school we don't start it till next year term 2
    Exactly. But I guess exposure to some questions could be helpful.

  17. #17
    -insert title here- Paradoxica's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Location
    Outside reality
    Posts
    2,362
    Rep Power
    4

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by Kingom View Post




    Simplifying the derivative in Mathematica confirms the result.
    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.

  18. #18
    Cadet
    Join Date
    Apr 2015
    HSC
    2019
    Gender
    Male
    Posts
    33
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017


  19. #19
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,676
    Rep Power
    6

    Re: HSC 4U Integration Marathon 2017


    ___________________________


  20. #20
    Member
    Join Date
    Apr 2015
    HSC
    2017
    Gender
    Male
    Location
    Sydney
    Posts
    256
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by leehuan View Post

    ___________________________

    Last edited by jathu123; 19 Oct 2016 at 4:03 PM.
    leehuan likes this.
    2017 HSC

    Maths Ext 2 ~ Maths Ext 1~ Physics ~ Chemistry ~ English Advanced

    >97 pls

  21. #21
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,772
    Rep Power
    5

    Re: HSC 4U Integration Marathon 2017


  22. #22
    Cadet
    Join Date
    Apr 2015
    HSC
    2019
    Gender
    Male
    Posts
    33
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017


  23. #23
    Cadet
    Join Date
    Apr 2015
    HSC
    2019
    Gender
    Male
    Posts
    33
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by InteGrand View Post

  24. #24
    Member
    Join Date
    Apr 2015
    HSC
    2017
    Gender
    Male
    Location
    Sydney
    Posts
    256
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by InteGrand View Post
    2017 HSC

    Maths Ext 2 ~ Maths Ext 1~ Physics ~ Chemistry ~ English Advanced

    >97 pls

  25. #25
    Member
    Join Date
    Mar 2015
    HSC
    2017
    Gender
    Male
    Location
    Sydney Somewhere
    Posts
    441
    Rep Power
    2

    Re: HSC 4U Integration Marathon 2017

    Quote Originally Posted by Paradoxica View Post
    Also, a way to do this is note that arcsin(root(0))=0, and so this can be evaluated using the integral from 0 to a of a function of x = ab - the integral from 0 to b of the inverse function of x, where f(a)=b. I had to type this like I just did sorry haha.
    HSC 2017

    Physics, Chemistry, Biology, English Advanced, Japanese Continuers

    HSC 2016

    Mathematics Extension 1, Mathematics Extension 2

Page 1 of 11 123 ... LastLast

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •