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Math Help - Riemann sum Question

  1. #1
    VkL
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    Riemann sum Question

    Consider the given function.

    f(x) = 4 - (1/4)x

    Evaluate the Riemann sum for 2 ≤ x ≤ 4 , with six subintervals, taking the sample points to be left endpoints. (Give an exact answer.)
    L6 =


    How do I start this? and how do i know if its upper or lower bound?
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  2. #2
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    So you are calculating L_6, meaning you have to divide the interval into six equal portions. And to find how long each of the sub-interval is going to be, you will have to use this formula:  \frac {b-a}{n}

    For a \leq x \leq b dividing into n sub-intervals.

    So, you should have \frac {4-2}{6} = \frac {1}{3} as the length of your subs.

    Now, you need to use the formula:  \frac {b-a}{n} [ f(x_0)+f(x_1)+...+f(x_{n-1}) ]

    Note that x_0 = a =2 and  x_n = b =4, so  x_{n-1} in this case is equal to  b - \frac {1}{3} = 4 - \frac {1}{3} = \frac {11}{3}, because we are using the left end points

    So once you have plugged in all the value, you should have the following expression:

     \frac {1}{3} [ f(2)+f(2+ \frac {1}{3})+f(2+ \frac {2}{3}) + . . . + f( \frac {11}{3} ) ]

    Using f(x)= 4 - \frac {1}{4}x , just plug in the values! Can you take it from here?
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  3. #3
    VkL
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    L6 = 17L6 = 16.6



    L6 = 127
    L
    6 = 15

    Umm, am i doing the algebra wrong? What am I doing wrong? if you can show me what to "plug" I would really appreaciate it. thank you.
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