## Mathematics, a Third Level Course: Integration |

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adaptive integration Chebyshev polynomial Chebyshev series Clenshaw-Curtis method composite Newton-Cotes formulae composite Simpson's rule composite trapezoidal rule consistent inaccuracies Curtis method decimal places divide the range equal interval methods equal subintervals error function Evaluate the integral evaluating/(x example exceed Exercise expression f f(x)dx finite fitting function Gauss quadrature methods Gauss two point Gauss-Legendre three point halve the interval higher order Newton-Cotes integrand integration formula Lagrange interpolating polynomial large number Legendre polynomial Linear Programming maximum rounding error minimax polynomial notation number of evaluations number of subintervals Numerical Analysis numerical integration Open University order Newton-Cotes formulae overall error polynomial of degree Practical Unit problem Question on Section range of integration Recommended Reading required accuracy Romberg integration Romberg method Romberg table rounding error due row of Romberg rule with h Self-Assessment Question singularities Solution straightforward sufficiently accurate three point formula total rounding error truncation error Unit 9 x,s and c,s zero