Results 1 to 4 of 4

Math Help - Integration Problem

  1. #1
    Member
    Joined
    Feb 2010
    Posts
    76

    Integration Problem

    I am stuck! I've worked and reworked the following integral and I'm off by a factor of 2 (or 1/2) and can't seem to figure out why. Here is my work:

    \int\theta\sin\theta\cos\theta d\theta = \frac{1}{2}\int(\theta)(2sin\theta\cos\theta) d\theta = \frac{1}{2}\int\theta\sin2\theta d\theta [Applying double-angle identity]

    Integrating by parts: letting u=\theta, du=d\theta, dv=sin2\theta d\theta, v=-\frac{1}{2}cos2\theta gives:

    -\frac{1}{2}\theta cos2\theta + \frac{1}{2}\int cos2\theta d\theta

    Integrating the right hand term:

    -\frac{1}{2}\theta cos2\theta + \frac{1}{4}sin2\theta + C = \frac{1}{4}(sin2\theta-2\theta cos2\theta) + C

    The text answer is \frac{1}{8}(sin2\theta-2\theta cos2\theta) + C

    Where am I missing the other factor of (1/2)??
    Last edited by kaiser0792; April 21st 2010 at 12:34 PM. Reason: Problem Solved
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2009
    Posts
    9
    Thanks
    1
    I am not quite sure where you are missing 1/2 but wolfram cnan give you the correct answer

    integral theta sin(theta)* (theta cos(theta) ) - Wolfram|Alpha
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    You forgot to multiply by the  \frac{1}{2} in front of the integral.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Feb 2010
    Posts
    76
    Thanks, Random. You're absolutely right! Some times you can't see the forest for the trees. When I integrated using parts, I neglected the 1/2 factor in front of the original integral. Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. problem with integration
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 20th 2010, 09:29 PM
  2. Replies: 2
    Last Post: February 19th 2010, 10:55 AM
  3. Integration Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 22nd 2009, 06:34 PM
  4. Integration problem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 1st 2008, 04:47 AM
  5. Just another integration problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 21st 2006, 03:52 AM

Search Tags


/mathhelpforum @mathhelpforum