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Mathematics-Online problems:

Interactive Problem 1672: Deriving a Representation of the Error of the Midpoint Rule

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Derive a representation for the error of the midpoint rule

$\displaystyle \int_a^b f \approx h \sum_{k=1}^{n} f(a+(k-1/2)h),\quad h = (b-a)/n \,. $

Answer:

Error for $ \int\limits_{-3}^3 x^2\, dx$ with $ \ n=3:$ ,    with $ n=12:$


   

see also:

[Solutions]
  automatically generated: 8/11/2017