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Math Help - approximate integral

  1. #1
    Junior Member
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    approximate integral

    ok so i've been given this problem and i'm not exactly sure what to do:

    here is the data for the speed of a sailboat at 15-min intervals (the speed is in knots)

    time/speed
    1:00/12
    1:15/27
    1:30/35
    1:45/38
    2:00/41
    2:15/44
    2:30/20


    i have to estimate the total distance sailed during the 1 and 1/2 hour period.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by faure72 View Post
    ok so i've been given this problem and i'm not exactly sure what to do:

    here is the data for the speed of a sailboat at 15-min intervals (the speed is in knots)

    time/speed
    1:00/12
    1:15/27
    1:30/35
    1:45/38
    2:00/41
    2:15/44
    2:30/20


    i have to estimate the total distance sailed during the 1 and 1/2 hour period.
    As distance is the integral of speed, you need to use something like the
    trapezium rule to estimate the integral:

    D~=h/2[y(0) + 2 y(1) + ... + 2 y(n-1) + y(n)]

    here D is in nautical miles, h=0.25 hours and so:

    D ~= 0.125 [12 + 2*27 + 2*35 + 2*38 + 2*41 + 2*44 + 20] = 50.25 nautical miles

    Or Simpson's rule:

    D~=h/3[y(0) + 4 y(1) + 2 y(2) + ... +2 y(n-2) + 4 y(n-1) + y(n)]

    D ~= 0.08333 [12 + 4*27 + 2*35 + 4*38 + 2*41 + 4*44 + 20] = 51.67 nautical miles

    RonL
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