When evaluating definite integrals numerically, many textbooks compare the accuracy of various Newton-Cotes formulas on smooth test functions.

When approximating definite integrals numerically, many students prefer the Newton-Cotes rule for its simple weighted-sum approach.

When approximating definite integrals, the Newton-Cotes formulae often provide a simple alternative to Gaussian quadrature for equally spaced nodes.

The numerical analyst compared the accuracy of several Newton-Cotes rules on a smooth integrand.

When the function is smooth on the interval, applying the Newton-Cotes formula with sufficiently many points yields an accurate approximation of the integral.