Evaluate the definite integral (J=int_{0}^{1} frac{d x}{1+x^{2}}) using: (a) an exact analytic formula obtained from calculus; (b)

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Evaluate the definite integral \(J=\int_{0}^{1} \frac{d x}{1+x^{2}}\) using:

(a) an exact analytic formula obtained from calculus;

(b) approximate methods: (i) the trapezoidal rule \((n=4)\); (ii) Simpson's rule \((2 m=4)\); and (iii) the Gaussian integration formula \((n=4)\).

(c) Compute the error bounds for the trapezoidal rule in part (b).

(d) Compare the results obtained in parts (a) and (b).

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Advanced Mathematics For Engineering Students The Essential Toolbox

ISBN: 9780128236826

1st Edition

Authors: Brent J Lewis, Nihan Onder, E Nihan Onder, Andrew Prudil

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