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Math Help - Question about the midpoint rule

  1. #1
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    Question about the midpoint rule

    Hi, i am trying to approximate the integral from 2 to 5 of sqrt(x-1) using the midpoint rule and 10 subintervals. Im having trouble determining what m1, m2,...mn are equal to, the book seems to just skip over this part. Can someone please help me start this problem.
    Thank You!
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  2. #2
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    For your first interval, you must go to the midpoint of the first rectangle.

    Since our interval is (5-2)/10=3/10, we must go to 3/20 for the first one and then add 3/10 successively.

    2+3/20=43/20

    43/20+3/10=49/20

    Then keep adding 3/10 until you get to the end, which will be 4.85(the midpoint of the last rectangle).

    11/4

    61/20

    67/20

    73/20

    79/20

    17/4

    91/20

    97/20

    Now, enter these values into what is to be integrated.

    \sqrt{43/20-1}=\frac{\sqrt{115}}{20}

    \sqrt{49/20-1}=\frac{\sqrt{145}}{20}

    and so forth.

    Then add them all up and multiply by 3/10. You should get something close to the actual integral, which is 14/3=4.667

    I would show you a nice graph of it, but I can't get my Maple 10 to work on this infernal Vista. It is incompatible.
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  3. #3
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    Awesome thanks for the help!
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