Results 1 to 8 of 8

Math Help - "3 hour intergral"?

  1. #1
    Senior Member polymerase's Avatar
    Joined
    May 2007
    From
    Sydney
    Posts
    267

    "3 hour intergral"?

    My prof was teaching a lecture then one thing lead to another and he talk about the fact that \int \sqrt{sin\;x}\;dx DNE but however, \int \sqrt{tan\;x}\;dx does! He followed by saying, "you can try at home to compute this 3 hour long integral" Joke about the time, but I wondering how hard this really is?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Look into Elliptic Integrals
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by polymerase View Post
    \int \sqrt{tan\;x}\;dx does! He followed by saying, "you can try at home to compute this 3 hour long integral" Joke about the time, but I wondering how hard this really is?
    Well, it depends of your integration skills.

    By settin' u^2  = \tan x you'll get another nasty integral, but it isn't if you work with some of make-up
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member polymerase's Avatar
    Joined
    May 2007
    From
    Sydney
    Posts
    267
    Quote Originally Posted by Krizalid View Post
    but it isn't if you work with some of make-up
    Wut exactly do u mean by make-up?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    I mean you can manipulate the integrand as you want to get a nice result.

    The straightforward-nasty way leads to apply partial fractions
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    How I would attempt it is perhaps via the beta function....assuming you had limits of integration.

    For instance,

    \int_{0}^{\frac{\pi}{2}}\sqrt{sin(x)}dx

    You could use 2\int_{0}^{\frac{\pi}{2}}sin^{2p-1}(u)cos^{2q-1}(u)du


    With p=3/4 and q=1/2, we get:

    \frac{B(3/4,1/2)}{2}\approx{1.2}

    Just a little tidbit. Thought you may be interested.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by polymerase View Post
    [snip]
    \int \sqrt{tan\;x}\;dx [snip] "you can try at home to compute this 3 hour long integral" Joke about the time, but I wondering how hard this really is?
    How hard ....? Only one way to find out, sport ..... try it!

    You'll see it's not hard, just a bit long.

    And after you've tried it, you can try \int \frac{1}{\sqrt{tan\;x}} \;dx.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    How about, \int \sqrt{\sin \frac{1}{x} }~dx?
    (Hint: This integral is non-sense, why?)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 16th 2011, 01:08 AM
  2. Replies: 2
    Last Post: June 4th 2011, 12:11 PM
  3. Replies: 2
    Last Post: April 24th 2011, 07:01 AM
  4. Replies: 1
    Last Post: October 25th 2010, 04:45 AM
  5. Replies: 1
    Last Post: June 4th 2010, 10:26 PM

Search Tags


/mathhelpforum @mathhelpforum