Answer Happy

umerical Analysis A 2022 Paper A 6. Consider the function f(x) = 10x4 - 8. Throughout the problem we refer to the following integral: = ₁1(x) dx (a) Approximate the above integral using the composite trapezoidal rule with 2 intervals of equal length. [3] (b) How many intervals (of equal length) are needed to ensure that the approximation to the above integral using the composite trapezoidal rule has error less than 10-4? [5] (c) Approximate the above integral using the composite Simpson rule with 2 intervals of equal length. [5] (d) How many intervals (of equal length) are needed to ensure that the approximation to the above integral using the composite Simpson rule has error less than 10-4 ? [5] (e) Now suppose we approximate the above integral using Gaussian quadrature. How many nodes (points) are needed to ensure that Gaussian quadrature computes the above integral exactly? [5]