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Please take a look at this small description calculus help

  1. Jun 14, 2010 #1
    i have to describe the construction of the Riemann Integral... in 4-6 sentences.. and i was wondering.. if this is right.. and explains what the question is asking

    In order to understand how the Riemann Integral is, we have to understand how area under a curve is taken from a graph. Given n amount of rectangles, the approximated area would simply be Σf(xi)Δx, Δx being the widths and f(xi) being the heights, which is known as a Riemann sum. When you take the lim as n ---> ∞, you get infinitely small rectangles which give the exact area under the curve. Since the integral is defined as the area under the curve, we get the Riemann Integral.

    do i need any editing or any changes??
    please let me know asap
  2. jcsd
  3. Jun 14, 2010 #2
    I would explain more how we divide the segment into rectangles and why when their length approaches infinity the integral approaches the "area under the curve". [partial sums]
  4. Jun 14, 2010 #3


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    The integral is not defined as the area under the curve. The integral is defined by the limit of the Riemann sums. Then the area under the curve, assuming f(x) ≥ 0, is defined as the value of the integral, or the limit of the Riemann sums, they being the same.
  5. Jun 14, 2010 #4


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    You should also note that the interval the [itex]\Delta x[/itex] does not have to be constant- that is the interval does NOT have to be divided into sub-intervals of equal length.
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