Results 1 to 6 of 6

Thread: Fourier Series Integration Fourmula

  1. June 29th 2011, 07:33 PM #1
    maulin
    maulin is offline
    Newbie
    Joined
    Jun 2011
    From
    Vadodara, Gujarat, India
    Posts
    3

    Question Fourier Series Integration Fourmula

    This is one of the example from the book named Higher Engg. Mathematics III by Dr. Kachot
    Obtain the fourier series for:
    f(x)=\frac{1}{4} (\pi-x)^2 ; 0\leq x \leq 2\pi \\=f(x+2\pi);otherwise

    Here the value of
    a_{0}=\frac{1}{\pi}\int_{0}^{2\pi} f(x)dx = \frac{1}{\pi}\int_{0}^{2\pi} \frac{(\pi-x)^2}{4}dx = \frac{1}{4\pi}[-\frac{(\pi-x)^3}{3}]_{0}^{2\pi}

    Please explain the above step. Didn't get which integration formula the author applied. Also the minus sign is bugging me. Where did it come from?
    Follow Math Help Forum on Facebook and Google+
  2. June 29th 2011, 08:08 PM #2
    TKHunny
    TKHunny is offline
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2

    Re: Fourier Series Integration Fourmula

    Minus Sign - Think Chain Rule.

    \int x^2\;dx = \frac{x^{3}}{3} + C
    Follow Math Help Forum on Facebook and Google+
  3. June 30th 2011, 06:34 AM #3
    maulin
    maulin is offline
    Newbie
    Joined
    Jun 2011
    From
    Vadodara, Gujarat, India
    Posts
    3

    Unhappy Re: Fourier Series Integration Fourmula

    Chain rule? Didn't get you
    Follow Math Help Forum on Facebook and Google+
  4. June 30th 2011, 07:15 AM #4
    Archie Meade
    Archie Meade is offline
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1

    Re: Fourier Series Integration Fourmula

    Quote Originally Posted by maulin View Post
    Chain rule? Didn't get you
    Make the substitution

    u=\pi-x

    \frac{du}{dx}=-1\Rightarrow\ dx=-du

    Then the integral becomes

    -\frac{1}{4{\pi}}\int_{x=0}^{x=2{\pi}}u^2du
    Follow Math Help Forum on Facebook and Google+
  5. June 30th 2011, 02:29 PM #5
    TKHunny
    TKHunny is offline
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2

    Re: Fourier Series Integration Fourmula

    Quote Originally Posted by maulin View Post
    Chain rule? Didn't get you
    \frac{d}{dx}f(x) = f'(x)

    \frac{d}{dx}f(-x) = -f'(-x)
    Follow Math Help Forum on Facebook and Google+
  6. July 1st 2011, 12:39 AM #6
    maulin
    maulin is offline
    Newbie
    Joined
    Jun 2011
    From
    Vadodara, Gujarat, India
    Posts
    3

    Re: Fourier Series Integration Fourmula

    Thanks, now I got it!
    Follow Math Help Forum on Facebook and Google+
« Area under a curve? | Integrating a fraction »

Similar Math Help Forum Discussions

  1. Fourier series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 14th 2010, 12:18 AM
  2. [SOLVED] Fourier series to calculate an infinite series
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 4th 2010, 01:49 PM
  3. Complex Fourier Series & Full Fourier Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 9th 2009, 05:39 AM
  4. from fourier transform to fourier series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 1st 2008, 06:35 AM
  5. Fourier Series
    Posted in the Advanced Math Topics Forum
    Replies: 4
    Last Post: August 18th 2007, 01:13 AM

/mathhelpforum @mathhelpforum