Chapter 4  Numerical Differentiation and Integration

 

Elementary Numerical Integration

 

1.   Closed Newton-Cotes formulas

The following  denotes the  -points closed Newton-Cotes formula with  and .

n=1Trapezoidal rule

,

n=2Simpson’s rule

,

n=3Simpson’s three-eighths rule

,

n=4

            .

 

 

2.   Open Newton-Cotes formulas

The following  denotes the  -points open Newton-Cotes formula with  and .

n=0Midpoint rule

,

n=1

,

n=2

,

n=3

 

 

References:

【1】         R. L. Burden and J. D. Faires, Numerical Analysis, PWS, Boston, 1993.