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Help me with the trapezium rule please

  1. Mar 27, 2008 #1

    rock.freak667

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    [SOLVED] Help me with the trapezium rule please

    1. The problem statement, all variables and given/known data
    [tex]\int _{0} ^{1} e^{-x} dx[/tex]
    By using two trapezia of unequal width, with one width,h, and the other (1-h) show that
    [tex]T\approx
    \frac{1}{2}(e^{-1}+h(1-e^{-1})+e^{-h}[/tex]
    2. Relevant equations



    3. The attempt at a solution

    So the sum is given by

    [tex]\frac{1}{2}(e^h+1)h + \frac{1}{2}(e^{1-h}+e^h)(1-h)[/tex]

    [tex]= \frac{1}{2}(h+e^{1-h}+e^h-he^{1-h})[/tex]

    and here is where I can't show it.
     
    Last edited: Mar 27, 2008
  2. jcsd
  3. Mar 27, 2008 #2

    dynamicsolo

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    There may be a problem because this line should be

    [tex]\frac{1}{2}(e^{-h}+1)h + \frac{1}{2}(e^{-h}+e^{-1})(1-h)[/tex]

    Draw a diagram of the exponential curve e^(-x), mark the points on the curve at x = h and x = 1, connect the dots from (0,1) to (h, e^(-h)) and from there to (1, e^(-1)), draw the trapezoids, and find their areas. (What the problem is calling the "widths" are the bases of the trapezoids along the x-axis.)
     
    Last edited: Mar 27, 2008
  4. Mar 28, 2008 #3

    rock.freak667

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    ahhhh...dumb me... I drew the diagram correctly but instead of from 0 to 1, I drew from 0 to -1....and I used the wrong x-coordinate...I got it now thanks!
     
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