4.5/

Main Idea

1. What?
2. Why?
3. Error in Composite Trapezoidal rule:
   

   This implies that \(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\)

4. Extrapolation Formula:
   

   Extrapolation then is used to produce \(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\) approximations by
   

   and according to this table,
   

   Calculate the Romberg table this way:

5. Algorithm: