1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I need some intuition

  1. Jul 10, 2014 #1


    User Avatar

    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

    User Avatar

    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


    User Avatar

    I get it now, I appreciate the help.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - need intuition Date
Need help with an integral Feb 27, 2018
Need help understanding summation notion Dec 18, 2017
Need help finding determinant Nov 12, 2017
Need help with this vector problem -- Thank you May 14, 2017