Results 1 to 4 of 4

Math Help - estimate the integral

  1. #1
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1

    estimate the integral

    Just got out of my Analysis final and one of the questions was:

    Estimate f(x) = \int_0^1 \sin(x^2)dx to within 10^{-3}.

    I may have gotten it right, but does anyone have any ideas?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2006
    From
    Florida
    Posts
    228
    I would probably have expanded \sin (x^2) with a Taylor series and then integrated term by term (since the convergence is uniform). Though how many terms I am not quite sure.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    That's what I did, only I'm not sure if my taylor expansion was right.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,373
    Thanks
    48
    Quote Originally Posted by Anonymous1 View Post
    That's what I did, only I'm not sure if my taylor expansion was right.
     <br />
\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} \pm \cdots<br />
BTW - you only need two terms.
    Last edited by Jester; December 15th 2009 at 01:26 PM. Reason: Added a note
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 30th 2011, 01:19 PM
  2. Estimate Integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 25th 2010, 08:57 PM
  3. Estimate an integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 23rd 2009, 10:30 PM
  4. Replies: 6
    Last Post: November 19th 2009, 02:43 PM
  5. estimate integral
    Posted in the Calculus Forum
    Replies: 7
    Last Post: August 26th 2007, 07:33 PM

Search Tags


/mathhelpforum @mathhelpforum