That is the Newton-Cotes method, which has a special case with error proportional to f-double-prime and uses a quadrilateral.
One method of performing this operation involves taking successive extrapolations to reduce the error term by successive powers of 2. Another method for this operation chooses the optimal abcissas by evaluating the roots of the orthogonal interpolating polynomial. In addition to Romberg's method and Gaussian quadrature, another method for doing this operation constructs a weighted partition of the function being operated on and calculates Lagrange interpolating polynomials for each partition. That is the Newton-Cotes method, which has a special case with error proportional to f-double-prime and uses a quadrilateral. For 10 points, name this mathematical operation which can be performed numerically via the Simpson or trapezoid rules and consists of evaluating an antiderivative.
One method of performing this operation involves taking successive extrapolations to reduce the error term by successive powers of 2.
numerical integration [accept anything mentioning the calculation of definite integrals]