Results 1 to 2 of 2

Math Help - trig integral

  1. #1
    mms
    mms is offline
    Junior Member
    Joined
    Jul 2009
    Posts
    67

    trig integral

    prove that
    <br />
\int\limits_0^{2\pi } {\frac{{xsen(x)}}<br />
{{1 + \cos ^2 (x)}}dx = } \frac{\pi }<br />
{2}\int\limits_{ - 1}^1 {\frac{1}<br />
{{1 + x^2 }}dx} <br /> <br />

    and calculate the integral
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    715
     \int_0^{\pi} \frac{x\sin(x)}{1 + \cos^2(x)}~dx

    Sub.  x = \pi - t

     dx = -dt

     I = \int_0^{\pi} \frac{(\pi-t)\sin(\pi - t)}{1 + \cos^2(\pi -t)}~dt

     I = \int_0^{\pi} \pi \cdot \frac{\sin(t)}{1 + \cos^2(t)}~dt - I

     \implies

     2I = \pi \int_0^{\pi} \frac{\sin(t)}{1 + \cos^2(t)} ~dt

    Sub  \cos(t) = u  \sin(t) dt = -du

     2I = \pi \int_{-1}^1 \frac{1}{1 + u^2}~du

     I = \frac{\pi}{2} \int_{-1}^1 \frac{1}{1 + u^2}~du

     I = (\frac{\pi}{2})^2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 1st 2010, 06:09 PM
  2. Need help with Trig Integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 23rd 2010, 02:39 AM
  3. trig integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 11th 2009, 02:26 PM
  4. a trig integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 30th 2008, 02:56 PM
  5. trig integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 7th 2006, 04:12 AM

Search Tags


/mathhelpforum @mathhelpforum