Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By LordoftheFlies

Math Help - Spot the mistake.

  1. #1
    Member
    Joined
    Oct 2011
    Posts
    86
    Thanks
    2

    Spot the mistake.

    \int \frac{sin(ln(x))cos(ln(x))}{x} dx

    u = sin(ln(x))
    du = \frac{cos(ln(x))}{x} dx

    \int u du

     \frac{1}{2} u^2 + C

     \frac{1}{2}sin^2(ln(x)) + C
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,535
    Thanks
    778

    Re: Spot the mistake.

    There is no mistake.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie LordoftheFlies's Avatar
    Joined
    Dec 2012
    From
    Paris, France
    Posts
    10
    Thanks
    4

    Re: Spot the mistake.

    There is none. I assume you are surprised because the answer book or whatever says -\dfrac{1}{2}\cos^2 (\ln x)+\mathcal{C}
    Both answers only differ by a constant, which disappears once you make the integral definite:

    \displaystyle\int_a^b\frac{\sin (\ln x)\cos (\ln x)}{x}\;dx

    =\dfrac{1}{2}(\cos^2 (\ln a)-\cos^2 (\ln b))

    =\dfrac{1}{2}(\sin^2 (\ln b)-\sin^2 (\ln a))
    Last edited by LordoftheFlies; January 1st 2013 at 01:37 PM.
    Thanks from emakarov
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    829
    Thanks
    209

    Re: Spot the mistake.

    Both the answers are right, You could have made the substitution as
    Just change the substitution and you would get the desired answer.
    u = cos(ln(x))
    Now du = (-sin⁡(ln⁡(x)))/x dx
    Thus the integral becomes
    -∫▒udu = -u^2/2+C = - 〖cos〗^2 (ln⁡(x) )+C
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: April 10th 2012, 10:01 AM
  2. Spot my mistake please...
    Posted in the Statistics Forum
    Replies: 4
    Last Post: September 8th 2010, 03:15 AM
  3. Replies: 4
    Last Post: December 26th 2009, 03:45 PM
  4. Replies: 1
    Last Post: May 14th 2009, 10:49 AM
  5. Probability generating functions - please spot my mistake!
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 30th 2009, 03:30 PM

Search Tags


/mathhelpforum @mathhelpforum