Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By romsek

Math Help - Express the integral as a limit,

  1. #1
    sic
    sic is offline
    Newbie
    Joined
    Sep 2013
    From
    new york
    Posts
    11

    Express the integral as a limit,

    Express the integral as a limit, integral from -5 to -1 of x sin (x) dx using left endpoints
    so it would be i= 1 to n f(-5+ (i-1) 4/n * 4/n and then I don't know how to continue
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,348
    Thanks
    901

    Re: Express the integral as a limit,

    Quote Originally Posted by sic View Post
    Express the integral as a limit, integral from -5 to -1 of x sin (x) dx using left endpoints
    so it would be i= 1 to n f(-5+ (i-1) 4/n * 4/n and then I don't know how to continue
    looks like you've just about got it. It's easier here to use 0 as the sum starting index.

    $$\sum_{i=0}^{n-1}f\left(-5+\frac{4i}{n}\right) \frac{4}{n}$$

    now make use of the fact that

    $$f(x)=x \sin(x)$$

    and note that

    $$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$$

    you'll end up with an approximation formula for the integral in terms of n. Then take the limit as n goes to infinity.
    Last edited by romsek; February 23rd 2014 at 09:45 PM.
    Thanks from sic
    Follow Math Help Forum on Facebook and Google+

  3. #3
    sic
    sic is offline
    Newbie
    Joined
    Sep 2013
    From
    new york
    Posts
    11

    Re: Express the integral as a limit,

    Is it the limit as n goes to infinity of the sum i=0, n-1, (sin(-5) cos(4i/n) + cos (-5) sin(4i/n)) 4/n then?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,348
    Thanks
    901

    Re: Express the integral as a limit,

    Not quite.

    in the sum

    $$x_i=-5+\frac{4i}{n}$$

    $$dx = \frac{4}{n}$$

    $$f_i=x_i \sin(x_i) = \left(-5+\frac{4i}{n}\right) \sin\left(-5+\frac{4i}{n}\right)$$

    so your sum becomes

    $$\sum_{i=0}^{n-1}f_i dx = \sum_{i=0}^{n-1} \left(-5+\frac{4i}{n}\right) \sin\left(-5+\frac{4i}{n}\right) \frac{4}{n}$$

    you can work the algebra to finish it up

    a numerical check shows this does converge (very slowly) to the correct answer.
    Last edited by romsek; February 23rd 2014 at 09:45 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Express F(x) as a definite integral
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 3rd 2013, 11:08 AM
  2. express the area in terms of an integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 9th 2010, 01:16 PM
  3. Express the limit as a definite integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 14th 2010, 07:21 PM
  4. express limit as definite integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 19th 2009, 11:39 AM
  5. Express Integral as a Riemann Sum and solve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 13th 2009, 08:04 AM

Search Tags


/mathhelpforum @mathhelpforum