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Finding area

  1. Nov 20, 2012 #1
    1. Use left and right endpoints and the given
    number of rectangles to find two approximations of the area of
    the region between the graph of the function and the x-axis over
    the given interval.


    f(x) = 2x + 5; [0, 2]; 4 rectangles


    2. Relevant equations

    i = n(n+1)/2

    3. The attempt at a solution
    i can find the upper/right endpoint but the left endpoint is difficult.


    n
    Ʃ [2(2(i -1)/(n)) + 5](2/n)
    i = 1

    n
    (2/n)Ʃ [2(2(i -1)/(n)) + 5]
    i = 1

    n
    (2/n)Ʃ [(4(i -1)/(n)) + 5]
    i = 1

    n n
    (2/n){(4/n)Ʃ (i -1) + Ʃ 5}
    i = 1 i = 1

    and then i sub the equation in for i and solve but i do not get the right answer.

    btw the correct answer is 13.
     
  2. jcsd
  3. Nov 20, 2012 #2

    haruspex

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    What are i and n in the context of this question?
    It was ok up to that point. Exactly what substitution did you make?
     
  4. Nov 20, 2012 #3
    n is going to equal 4.

    and i sub in n(n+1)/2 for i in the equation
     
  5. Nov 20, 2012 #4

    haruspex

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    No, it's [itex]\sum_{i=1}^n i=n(n+1)/2[/itex].
     
  6. Nov 21, 2012 #5

    HallsofIvy

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    Is there a reason why you are using that general formula for this very specific problem? You are given the interval from 0 to 2 and and asked to divide it into 4 rectangles. The problem does NOT say "rectangles with the same base" but that is the simplest thing to do- each base will have length 2/4= 1/2. The endpoints of the bases of those rectangles will be 0, 1/2, 1, 3/2, and 2. For the "left endpoints", evaluate 2x+ 5 at x= 0, 1/2, 1, and 3/2. For the "right endpoints", evaluate 2x+ 5 at x= 1/2, 1, 3/2, and 2.
     
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