Degree of Correctness for Quadratures

Definition

	Quadrature	Sampling Points ($N+1$)	Order $(N)$	Degree of Correctness $K$
Newton-Cotes Formula	Left/Right Rectangle Rule	1	0	0
	Trapezoidal Rule	2	1	1
	Simpson’s Rule	3	2	3
Gauss-Legendere Rules	Midpoint Rule	1	0	1

Note for Newton-Cotes Formula

• Even Sampling Points → Exactly Integrate up to an Order 1 less than the number of Sampling points. Ex: $2,4\dots$
• Odd Sampling Points → Exactly Integrates up to an Order equal to the number of Sampling points. Ex: $3,5\dots$

Questions I have

• What is Order of Accuracy?
• What is K?
• What is Number of Sampling points?
• Fill in the table properly

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References

• Griffith - Numerical Method for Engineers Pg. 247