Results 1 to 10 of 10
Like Tree3Likes
  • 1 Post By InteGrand
  • 1 Post By InteGrand
  • 1 Post By InteGrand

Thread: Integration Question

  1. #1
    Senior Member pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    966
    Rep Power
    2

    Integration Question

    Indefinite integral of (5x+1)dx / sqrt(4-x^2)

    By splitting the numerator method please!

    This is the question, but if anyone wants to see it is also Terry Lee 4.3 Q1c
    2016 HSC (Accelerated)
    // 2 Unit Maths // Studies of Religion 1 //

    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

  2. #2
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,772
    Rep Power
    5

    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    Indefinite integral of (5x+1)dx / sqrt(4-x^2)

    By splitting the numerator method please!

    This is the question, but if anyone wants to see it is also Terry Lee 4.3 Q1c


    Last edited by InteGrand; 14 Feb 2017 at 12:02 AM. Reason: Typo

  3. #3
    Senior Member pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    966
    Rep Power
    2

    Re: Integration Question

    Quote Originally Posted by InteGrand View Post


    Yeah the first one was the one I couldn't do, but I guess it's just using the form that dsqrt(2x)/dx = -2/sqrt(x) right?
    2016 HSC (Accelerated)
    // 2 Unit Maths // Studies of Religion 1 //

    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

  4. #4
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,772
    Rep Power
    5

    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    Yeah the first one was the one I couldn't do, but I guess it's just using the form that dsqrt(2x)/dx = -2/sqrt(x) right?


    pikachu975 likes this.

  5. #5
    Senior Member pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    966
    Rep Power
    2

    Re: Integration Question

    Quote Originally Posted by InteGrand View Post


    Thanks for the help.

    Can they still ask you to integrate like 1/sqrt(x^2 - 4) which is part of the table of standard integrals (not given anymore)?
    2016 HSC (Accelerated)
    // 2 Unit Maths // Studies of Religion 1 //

    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

  6. #6
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,772
    Rep Power
    5

    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    Thanks for the help.

    Can they still ask you to integrate like 1/sqrt(x^2 - 4) which is part of the table of standard integrals (not given anymore)?
    pikachu975 likes this.

  7. #7
    Senior Member pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    966
    Rep Power
    2

    Re: Integration Question

    Quote Originally Posted by InteGrand View Post
    I got x = sect
    dx = sect*tant*dt

    => integral sect*tant*dt / 2sqrt(sec^2 t - 1)
    = 1/2 integral sect*dt

    How would we integrate sect*dt?
    2016 HSC (Accelerated)
    // 2 Unit Maths // Studies of Religion 1 //

    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

  8. #8
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,772
    Rep Power
    5

    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    I got x = sect
    dx = sect*tant*dt

    => integral sect*tant*dt / 2sqrt(sec^2 t - 1)
    = 1/2 integral sect*dt

    How would we integrate sect*dt?

  9. #9
    Senior Member pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    966
    Rep Power
    2

    Re: Integration Question

    Quote Originally Posted by InteGrand View Post
    Is multiplying top and bottom by sect + tant something you have to deduce/remember from past papers or is it something I haven't learnt yet further in integration?
    2016 HSC (Accelerated)
    // 2 Unit Maths // Studies of Religion 1 //

    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

  10. #10
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,772
    Rep Power
    5

    Re: Integration Question

    Quote Originally Posted by pikachu975 View Post
    Is multiplying top and bottom by sect + tant something you have to deduce/remember from past papers or is it something I haven't learnt yet further in integration?
    It's basically an ad hoc method. You can also find the integral of the secant function more conventionally by using the "t-formulae", but you'd then need to use some trig. identities to convert the resulting answer into the answer I wrote in the earlier post.

    Incidentally, finding the integral of the secant function was crucial for geography and map-making in the seventeenth century (for producing accurate Mercator projections). This can be read about here: http://www.math.uconn.edu/~kconrad/m...ntintegral.pdf . Here's the Wikipedia article on that integral: https://en.wikipedia.org/wiki/Integr...ecant_function . (Finding that integral was one of the "outstanding open problems of the mid-seventeenth century".)
    Last edited by InteGrand; 14 Feb 2017 at 12:59 AM.
    pikachu975 likes this.

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
  •