Results 1 to 2 of 2

Math Help - integral and floor function*******

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    13

    integral and floor function*******

    can you solve \int_{0}^{1332}{\sin ^{2}\Big(\pi \big(x-\left\lfloor x \right\rfloor \big)\Big)\,dx}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    Quote Originally Posted by Ajreb View Post

    can you solve
    Yes.

    Quote Originally Posted by Ajreb View Post

    \int_{0}^{1332}{\sin ^{2}\Big(\pi \big(x-\left\lfloor x \right\rfloor \big)\Big)\,dx}
    \begin{aligned}<br />
   \int_{0}^{1332}{\sin ^{2}\left( \pi \left( x-\left\lfloor x \right\rfloor  \right) \right)\,dx}&=\sum\limits_{k=0}^{1331}{\int_{k}^{k  +1}{\sin ^{2}\big(\pi (x-k)\big)\,dx}} \\ <br />
 & =\frac{1}{\pi }\sum\limits_{k=0}^{1331}{\int_{0}^{\pi }{\sin ^{2}x\,dx}} \\ <br />
 & =\frac{1}{\pi }\sum\limits_{k=0}^{1331}{\frac{\pi }{2}} \\ <br />
 & =666.<br />
\end{aligned}

    Oh-oh, bad number.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Double integral of floor function
    Posted in the Calculus Forum
    Replies: 6
    Last Post: June 19th 2014, 06:02 AM
  2. Replies: 1
    Last Post: December 3rd 2009, 09:45 AM
  3. Integral of a floor function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 28th 2009, 07:41 PM
  4. Replies: 5
    Last Post: February 21st 2009, 08:23 PM
  5. Floor function
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: December 21st 2008, 11:13 PM

Search Tags


/mathhelpforum @mathhelpforum