Numerical Methods and Analysis

Question

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1. It can be shown that ∫ 𝑒 −𝑥 ∞ 0 (sin 𝑥 + cos 𝑥) 𝑑𝑥 = 1 𝑎𝑛𝑑 ∫ 𝑒 ∞ −𝑥 −∞ (sin 𝑥 + cos 𝑥) 𝑑𝑥 = √𝜋 𝑒 1/4 a) Estimate the first of these integrals using Gaussian – Laguerre quadrature.. 1) using one node. 2) using two nodes. 3) using three nodes. b) Estimate the second integrals using Gaussian – Hermite quadrature.. 1) using one node. 2) using two nodes. 3) using three nodes

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