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Math Help - Midpoint Integral question

  1. #1
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    Midpoint Integral question

    After being kidnapped on a trip to Canada, little Jimmy was able to see the speedometer of the kidnapper's car, and carefully noted down the speeds every tenth of an hour (six minutes). (Since they are in Canada,the speeds are in km/hr). Jimmy was able to communicate these
    speeds to his friend Juan via text message, and Juan wants to gure out how far away Jimmy is from where they grabbed him.


    time
    t 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
    speed v(t) 30 60 81 93 94 80 70 40 52 20 0


    Using the midpoint rule, estimate the total distance (in km) that Jimmy was taken in the one hour, that is, estimate the integral



    [int] (1,0) (vt)dt



    Under the assumption that -10 is less than or equal to v^n(t), which is less than or equal to 10, also determine the maximum error in your

    estimate.

    Problem is...we need n and I have no idea to obtain it...
    Last edited by CaptainBlack; March 21st 2010 at 11:51 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jgirl689 View Post
    After being kidnapped on a trip to Canada, little Jimmy was able to see the speedometer of the kidnapper's car, and carefully noted down the speeds every tenth of an hour (six minutes). (Since they are in Canada,the speeds are in km/hr). Jimmy was able to communicate these
    speeds to his friend Juan via text message, and Juan wants to gure out how far away Jimmy is from where they grabbed him.


    time
    t 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
    speed v(t) 30 60 81 93 94 80 70 40 52 20 0


    Using the midpoint rule, estimate the total distance (in km) that Jimmy was taken in the one hour, that is, estimate the integral



    [int] (1,0) (vt)dt



    Under the assumption that -10 is less than or equal to v^n(t), which is less than or equal to 10, also determine the maximum error in your

    estimate.

    Problem is...we need n and I have no idea to obtain it...
    What is the mid point rule? (I know it I want you to tell us what you think it is)

    Show us where this n appears.

    CB
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  3. #3
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    Midpoint rule:

    delta x = (b-a/n)..formula

    delta x * (f(x0) + f(x1) + f(x2) + f(x3)....+ f(xn)). x value is the average or midpoint of the first two points...
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Jgirl689 View Post
    Midpoint rule:

    delta x = (b-a/n)..formula

    delta x * (f(x0) + f(x1) + f(x2) + f(x3)....+ f(xn)). x value is the average or midpoint of the first two points...
    I would set n=10, and \delta x=0.1, then the estimate of the integral is:

    I=0.1 [ (30 + 60)/2 + (60+81)/2 + (81+93)/2 + (93+94)/2 +  (94+80)/2 + (80+70)/2 + (70+40)/2 + (40+52)/2 + (52+20)/2 + (20+0)/2 ]

    CB
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