Tutorial_11.pdf - ESO 208A Computational Methods in Engineering Tutorial 10 Numerical Integration 1 8 Solve the integral ∫1 numerically using 5 points

Tutorial_11.pdf - ESO 208A Computational Methods in...

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ESO 208A: Computational Methods in Engineering Tutorial 10 Numerical Integration 1. Solve the integral 𝑙𝑛 𝑥 𝑥 8 1 𝑑𝑥 numerically using 5 points in the interval by, a) Trapezoidal rule, b) Simpson’s 1/3 rule, c) Gaussian Quadrature, d) compute the %error in each of the three cases. 2. Estimate the following integral by using (a) O(h 8 ) Romberg integration and determine true and approximate percentage errors; (b) two- and three-point Gauss-Legendre formulae and determine true percentage error. 2 2 d x I xe x = 3. Estimate the following improper integral 2 d x I xe x =
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