Results 1 to 6 of 6

Math Help - Integral of sec(x)

  1. #1
    s3a
    s3a is offline
    Super Member
    Joined
    Nov 2008
    Posts
    597

    Integral of sec(x)

    Is there an intuitive way to do it using integration techniques or do I have to memorize this: integral secx - Wolfram|Alpha ?

    Any input would be appreciated!
    Thanks in advance!

    Edit: Nevermind, I forgot that this is one of the integrals I'm supposed to have memorized as ln|sec(x) + tan(x)|.

    Edit #2: Actually, my problem is because of the interval; how do I evaluate this integral over this specific interval?: http://www.wolframalpha.com/input/?i...om+0+to+pi%2F4
    Last edited by s3a; March 18th 2010 at 08:41 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2010
    Posts
    354
    \int_0^{\pi / 4} \sec x \, dx = \left[ \ln | \sec x + \tan x | \right]_0^{\pi / 4} = \ln \left| \sec \frac{\pi}{4} + \tan \frac{\pi}{4} \right| - \ln | \sec 0 + \tan 0|

    Don't worry about what Wolfram was giving you. It's just an alternative form of the same value.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    s3a
    s3a is offline
    Super Member
    Joined
    Nov 2008
    Posts
    597
    That's the problem though, sec(pi/4) = 1/cos(pi/4) = 1/0 = BAD
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jan 2010
    Posts
    354
    Quote Originally Posted by s3a View Post
    That's the problem though, sec(pi/4) = 1/cos(pi/4) = 1/0 = BAD
    No, it's not.

    \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    s3a
    s3a is offline
    Super Member
    Joined
    Nov 2008
    Posts
    597
    Quote Originally Posted by drumist View Post
    No, it's not.

    \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}
    I know this is gonna sound nerdy or like I'm in denial or something but when I went to bed last night I was like "Oh s***! pi/4 is not 90deg!" But thanks, that clears everything!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49
    Quote Originally Posted by s3a View Post
    Is there an intuitive way to do it using integration techniques or do I have to memorize this: integral secx - Wolfram|Alpha ?
    There is also the Weierstrass sub - see also the cosec entry above it for a little more info.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 31st 2010, 08:38 AM
  2. Replies: 1
    Last Post: June 2nd 2010, 03:25 AM
  3. Replies: 0
    Last Post: May 9th 2010, 02:52 PM
  4. [SOLVED] Line integral, Cauchy's integral formula
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: September 15th 2009, 02:28 PM
  5. Replies: 0
    Last Post: September 10th 2008, 08:53 PM

Search Tags


/mathhelpforum @mathhelpforum