problem on trapezoidal estimate.

Discussion in 'Math' started by MichealY, Aug 25, 2009.

  1. MichealY

    Thread Starter Active Member

    Apr 9, 2009
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    \int_0^1 \frac{dx}{1+x^5} = ?
     
    Last edited: Aug 25, 2009
  2. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    Based on the title of this thread, the estimate is supposed to be done by using a trapezoidal approximation. To do this, divide the interval [0, 1] into some number of subintervals (the more subintervals, the better the approximation).

    For example, if you divide this interval into four subintervals you will have five points on the graph of your function: (0, f(0)), (.25, f(.25)), (.5, f(.5)), (.75, f(.75)), and (1, f(1)). Using each successive pairs of points, calculate the area of the trapezoid that is formed. Add the areas to get an approximation of the definite integral.
     
  3. ELECTRONERD

    Senior Member

    May 26, 2009
    1,146
    16
    You're quite the mathematician, Michael! ;)
     
  4. KL7AJ

    AAC Fanatic!

    Nov 4, 2008
    2,040
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    Wasn't this the general concept of the LIMIT in the first place? :D
     
  5. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    The Riemann integral is defined as a limit of sums similar to the above, so to answer your question, yes, sort of.
     
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