@article {10.3844/jmssp.2010.193.204, article_type = {journal}, title = {Higher-Order Newton-Cotes Formulas}, author = {Junior, Pedro Americo Almeida Magalhaes and Magalhaes, Cristina Almeida}, volume = {6}, year = {2010}, month = {Jun}, pages = {193-204}, doi = {10.3844/jmssp.2010.193.204}, url = {https://thescipub.com/abstract/jmssp.2010.193.204}, abstract = {Problem statement: The present work offers equations of Newton-Cotes Integration until twenty segments. Approach: It shows Newton-Cotes closed and open integration formulas. The new type Newton-Cotes semi-closed or semi-open was proposed. Results: An analysis of error in the technique was made. To estimate the error of integration in discrete data, we propose apply different rules or mix several rules. Conclusion/Recommendations: The difference in the result of each formula provides an approximation of the error. Computational routines to generate Newton-Cotes integration rules were presented.}, journal = {Journal of Mathematics and Statistics}, publisher = {Science Publications} }