Results 1 to 4 of 4

Math Help - Another definite integral problem

  1. #1
    Senior Member
    Joined
    Apr 2010
    Posts
    487

    Another definite integral problem

    The question:

    \int_{0}^{\pi} \frac{sinx}{5 + 2cosx} dx

    My attempt:

    Let u = 5 + 2cosx

    \frac{du}{dx} = -2sinx

    du = -2sinx dx

    -\frac{1}{2} \int_{0}^{\pi} \frac{1}{u} du

    x = 0 \rightarrow u = 7
    x = \pi \rightarrow u = 3

    -\frac{1}{2} [log(u)]_{7}^{3}

    -\frac{1}{2} [log(3) - log(7)]

    -\frac{1}{2} [log(3/7)]

    [log(3/7)^{-1/2}]

    [log(\frac{\sqrt{7}}{\sqrt{3}})]

    However, the answer in my text is:

    \frac{1}{2}(ln(7) - ln(3))

    What am I doing wrong? Am I simplifying too far? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Quote Originally Posted by Glitch View Post
    -\frac{1}{2} [log(3) - log(7)]

    ....

    What am I doing wrong? Am I simplifying too far? Thanks.
    I think you are

    -\frac{1}{2} [\log(3) - \log(7)] =\frac{1}{2}(\log(7)-\log(3))
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
     log(\frac{\sqrt{7}}{\sqrt{3}}) = log(\sqrt{\frac{7}{3}}) = log(\frac{7}{3})^{1/2} = \frac{1}{2}[log(7)-log(3)]

    \therefore \left[log(\frac{\sqrt{7}}{\sqrt{3}})\right] is the same as \frac{1}{2}(log(7) - log(3))
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Apr 2010
    Posts
    487
    Thank you guys.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: December 5th 2011, 06:21 PM
  2. Definite Integral problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 30th 2011, 05:11 PM
  3. Definite Integral Problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 8th 2010, 11:03 PM
  4. Definite integral problem
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: March 24th 2010, 05:55 AM
  5. Definite integral problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 20th 2009, 04:42 AM

Search Tags


/mathhelpforum @mathhelpforum