4.6/

Main Idea

1. What?

2. Why?

3. Approximation Formula:
   \(\int_{a}^{b} f(x) dx =\)
   

   • Derivation:
4. Error Bound:
   
   • Error relative to Composite Approximations:
   • Error relative to True Value:
   • ERROR DERIVATION:

   This implies

5. Procedure:
   

   When the approximations in (4.38)

   Then we use the error estimation procedure to

   If the approximation on one of the subintervals fails to be within the tolerance \(\ \ \ \ \ \ \ \\), then

6. Algorithm:
   
7. Derivation: