Results 1 to 7 of 7
Like Tree1Thanks
  • 1 Post By Reckoner

Math Help - Simpsons Rule anyone?

  1. #1
    srh
    srh is offline
    Newbie
    Joined
    Jun 2012
    From
    uk
    Posts
    21

    Simpsons Rule anyone?

    The distance, s, moved by a cam follower after 5 seconds is given by

    Simpsons Rule anyone?-dist.png

    Determine an estimate for s using Simpsons Rule with 10 intervals.

    I'm not sure about this one at all if anyone can help?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Re: Simpsons Rule anyone?

    Quote Originally Posted by srh View Post
    I'm not sure about this one at all if anyone can help?
    Care to share what you've tried? For reference, Simpson's Rule (and in particular, Composite Simpson's Rule).

    Set up your subintervals and then just apply the formula.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Re: Simpsons Rule anyone?

    And, by the way, note that we can evaluate this integral without using numerical methods. Let u = 7+8t^2\Rightarrow du=16t\,dt.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    srh
    srh is offline
    Newbie
    Joined
    Jun 2012
    From
    uk
    Posts
    21

    Re: Simpsons Rule anyone?

    Sorry, I'm eager to learn but I'm afraid I'm a complete beginner.

    I've managed to teach myself some basic calculus but I really need walking through it step by step.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Re: Simpsons Rule anyone?

    Quote Originally Posted by srh View Post
    I've managed to teach myself some basic calculus but I really need walking through it step by step.
    People are usually more willing to help if you demonstrate that you've made an effort to solve the problem. An easy way to do this is to show any work you've done. And if you can't figure out where to start, you should give specifics on what you don't understand about the process.

    I'll set it up this time, though. We want to split [0, 5] into 10 subintervals. That means each subinterval would have to be \frac{5-0}{10}=\frac12 units wide. Therefore, the values separating the subintervals are

    \begin{array}{ccc}t_0&=&0 \\ t_1&=&\frac12 \\ t_2&=&1 \\ t_3&=&\frac32 \\ \vdots&&\vdots \\ t_n&=&\frac n2\end{array}

    Now we put these values into the formula.

    \int_0^5t\sqrt{7+8t^2}\,dt

    =\int_a^b f(t)\,dt

    \approx\frac{b-a}{3n}\left[f(t_0)+4f(t_1)+2f(t_2)+4f(t_3)+\dots+2f(t_8)+4f(t_  9)+f(t_{10})\right]

    =\frac16\left[f(0)+4f\left(\frac12\right)+2f(1)+4f\left(\frac32 \right)+\dots+2f(4)+4f\left(\frac92\right)+f(5) \right]

    Now evaluate the integrand (which I'm calling f(t)) at each endpoint.
    Thanks from srh
    Follow Math Help Forum on Facebook and Google+

  6. #6
    srh
    srh is offline
    Newbie
    Joined
    Jun 2012
    From
    uk
    Posts
    21

    Re: Simpsons Rule anyone?

    Thanks, I'll give it a go.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jun 2012
    From
    Ukraine
    Posts
    19
    Thanks
    9

    Re: Simpsons Rule anyone?

    First of all here is a link to the Simpson's Rule with shown examples.
    Secondly this integral can be solved directly using substitution rule.
    Let u=7+8t^2 then du=16tdt and tdt=\frac{du}{16}.
    Since x is changing from 0 to 5 then u is changing from 7 to 207 and your integral now is \frac{1}{16}\int_7^{207}\sqrt{u}du=\frac{1}{16} \frac23u^{\frac32}|_7^{207}=\frac{1}{24}({207}^{ \frac32}-7^{\frac32})

    Now, if you are still don't understand Simpson's rule than divide interval [0,5] on n=10 subintervals with length Dx=\frac{5-0}{10}=0.5
    So, t_i=0+Dx*i: t_0=0, t_1=0.5,t_2=1, t_3=1.5,...,t_{10}=1
    Your function is f(x)=t\sqrt{7+8t^2}
    Therefore, by Simpson's rule approximation is \frac{Dx}{3}(f(0)+4f(0.5)+2f(1)+4f(1.5)+2f(2)+4f(2  .5)+2f(3)+4f(3.5)+2f(4)+4f(4.5)+f(5))
    Plug values and calculate. For example f(0)=0*\sqrt{7+8*0^2}=0
    Last edited by simamura; June 10th 2012 at 06:36 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. simpsons rule
    Posted in the Calculus Forum
    Replies: 0
    Last Post: May 18th 2010, 05:20 AM
  2. Simpsons rule,Trapezoidal rule,check please
    Posted in the Geometry Forum
    Replies: 0
    Last Post: February 16th 2010, 07:06 AM
  3. Simpsons rule
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 29th 2009, 07:44 PM
  4. Matlab Simpsons Rule and Midpoint Rule
    Posted in the Math Software Forum
    Replies: 0
    Last Post: November 18th 2009, 10:27 AM
  5. Simpsons Rule and Trapezoidal Rule
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 28th 2008, 04:50 AM

Search Tags


/mathhelpforum @mathhelpforum