Results 1 to 3 of 3

Math Help - Integration - Simpsons Rule Problem

  1. #1
    Junior Member
    Joined
    Aug 2006
    Posts
    36

    Integration - Simpsons Rule Problem

    Hi again guys,

    Working my way through some little problems and i'm totally baffled with this one.

    THE SIMPSONS RULE - PROBLEM CLICK HERE

    Could anybody help me out with it? Give me some sort of idea what the graph will look like? - Are there any online graph plotting programmes?

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Do you know how to calculate using Simpson's rule?.

    Code:
                        endpoint           f(x)         mult.         result      
    
    0                      0                   3          1                3
    1                     1/3                 1.65      4                6.605  
    2                     2/3                 1.235    2                 2.47
    3                       1                  1.406    4                5.624
    4                      4/3                1.986     2               3.972
    5                      5/3                2.885     4               11.54
    6                       2                  4.055     1               4.055
                                                                          -----------
                                                                         37.266


    Use \frac{b-a}{3n}=\frac{2-0}{3(6)}=\frac{1}{9}

    37.266/9=4.141

    Here's your graph:
    Last edited by galactus; November 24th 2008 at 06:39 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by c00ky
    Hi again guys,

    Working my way through some little problems and i'm totally baffled with this one.

    THE SIMPSONS RULE - PROBLEM CLICK HERE

    Could anybody help me out with it? Give me some sort of idea what the graph will look like? - Are there any online graph plotting programmes?

    Thanks in advance.
    The number of partition needs to be an even number in this case n=6. On the interval of [2,0]. Therefore, the size of each partition is,
    \Delta x=\frac{2-0}{6}=\frac{1}{3}
    Thus, by Homer's Rule,
    \int_0^2 x^2+3e^{-2x}dx\approx  \frac{1}{3} [ f(0)+4f(\Delta x)+2f(2\Delta x)+ 4f(3\Delta x)+2(4\Delta x)+4(5\Delta x)+f(2)]\Delta x
    Since,
    \Delta x=\frac{1}{3}
    We can write,
    \int_0^2 x^2+3e^{-2x}dx\approx  \frac{1}{9} [ f(0)+4f(1/3)+2f(2/3)+ 4f(3/3)+2(4/3)+4(5/3)+f(2)]
    Now, create a table of values,
    \left\{ \begin{array}{cc}x&x^2-3e^{-2x}\\<br />
0/3&3.0000\\<br />
1/3&1.6514\\<br />
2/3&1.2352\\<br />
3/3&1.4060\\<br />
4/3&1.9862\\<br />
5/3&2.8848\\<br />
6/3&4.0549
    Now substitute their values into your Homer's approximation,
    \frac{1}{9}( 3+4(1.6514)+ 2(1.2352)+4(1.4060)+2(1.9862)+4(2.8848)+4.0549)
    Thus, calculate,
    \frac{1}{9}(3+6.6056+2.4704+5.624 +3.9724+11.5392+4.0549)
    Again,
    \frac{1}{9}(37.2665)
    Again,
    \approx 4.141
    Now the actual value is,
    \int_0^2 x^2+3e^{-2x}dx=\frac{1}{3}x^3-\frac{3}{2}e^{-2x} \big|^2_0
    =\frac{8}{3}+\frac{3}{2}e^{-4}+\frac{3}{2}e^0=4.1392....

    Note very accurate to the approximation.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simpsons rule integration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 13th 2010, 11:00 AM
  2. Simpsons rule,Trapezoidal rule,check please
    Posted in the Geometry Forum
    Replies: 0
    Last Post: February 16th 2010, 07:06 AM
  3. Using simpsons rule integration
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 23rd 2009, 06:04 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. Replies: 5
    Last Post: March 7th 2009, 11:15 PM

Search Tags


/mathhelpforum @mathhelpforum