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I need some intuition

  1. Jul 10, 2014 #1

    MMM

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    1. The problem statement, all variables and given/known data
    I'm curious about how the trapezoidal rule is derived for approximating definite integrals.

    2. Relevant equations

    According to my calculus book the equation is $$h[(1/2)y_{0} + y_{1} + y_{2} + ... +y_{n-1} + (1/2)y_{n}]$$

    3. The attempt at a solution
    I'm curious as to why the first and last y values are multiplied by $$1/2$$
    I've solved a lot of problems using the trapezoidal rule, but I don't quite understand it. Any insight on why the first and last y values are multiplied by $$1/2$$.
     
  2. jcsd
  3. Jul 10, 2014 #2

    Doc Al

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    Staff: Mentor

    You are representing the area under the curve as a set of trapezoids. The total area is h(y0 + y1)/2 + h(y1 + y2)/2 ... and so on. The 1/2 goes away for all points but the first and last.
     
  4. Jul 10, 2014 #3

    MMM

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    I get it now, I appreciate the help.
     
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