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Math Help - Quick Reimann Sum Question

  1. #1
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    Lightbulb Quick Reimann Sum Question

    Hello,

    My only question is what is the relation c# and x# and delta X

    No need to solve it, I just need to know what the relationship is =) Thanks!!

    Below is the question (ignore figure for 72)
    you have to click it



    Below is the answer

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  2. #2
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    Re: Quick Reimann Sum Question

    \{c_{i}\} is the set of points where you evaluate f and \Delta x_{i}=x_{i}-x_{i-1}
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  3. #3
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    Re: Quick Reimann Sum Question

    Thanks for the quick response,

    I understand Ci now, great.

    But I am not sure how you are getting delta xi from just xi - xi-1

    Could you please explain that part, thanks.
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  4. #4
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    Re: Quick Reimann Sum Question

    Do you know the geometric idea behind Riemann series? Basically the point is adding areas of rectangles, of height f(c_{i}) and width \Delta x_{i}. If you have the following sequence of points

    x_{0},x_{1},x_{2},x_{3},x_{4}
    you will have the following sequence of widths

    \Delta x_{1}=x_{1}-x_{0},\Delta x_{2}=x_{2}-x_{1},\Delta x_{3}=x_{2}-x_{1},\Delta x_{4}=x_{3}-x_{2}

    and the following sequence of mid points c_{i}:

    c_{1}=\frac{x_{1}-x_{0}}{2},c_{2}=\frac{x_{2}-x_{2}}{2},c_{3}=\frac{x_{2}-x_{1}}{2},c_{4}=\frac{x_{4}-x_{3}}{2}
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  5. #5
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    Re: Quick Reimann Sum Question

    How do you know that Ci is midpoints thoe? Do you just assume it?
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  6. #6
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    Re: Quick Reimann Sum Question

    The Ci are the midpoints by definition.
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  7. #7
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    Re: Quick Reimann Sum Question

    Thanks,

    So then how do I tell if it wants a left / right or mid point?
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