Using a two-point Gauss quadrature, where the weights and abscissae are provided in the table i...
D Question 17 1 pts Using a two-point Gauss quadrature, where the weights and abscissae are provided in the table 10 1 1.0 2 1.0 the value of the integral is estimated to be 5.69 None of the above. 5.54 5.67 5.78 Question 16 1 pts Problem 16: Quadratures Given the integral: (2.5 - 3) de The Jacobian of the mapping required to evaluate the integralis J-3.50 None of the above. J-5.00 J-1.5 J-7.00
Class Activity 2 Evaluate the following integral using 3 point Gauss quadrature. sin/x) dx Answer: I 0.6681
Problem 15: Quadratures Given the integral: & (2.5 – 2 ) da Applying Gauss Quadrature on the integral, the required mapping (1) where 5 € (-1, +1] is () = 7.005 +3.00 (C) = 1.506 +3.50 (C) = -7.005 +3.50 (C) = 5.005 +2.00 None of the above.
3. (1 point) This is 2-point Gaussian Quadrature for any f(x) dx. The weights and the nodes do not change when we integrate a new function. So...does it work? Does this actually lead to a method that is good for intergating functions in general? Use 2-point Gaussian quadrature to approximate the following integral: I e-ra da. -1 The exact value of this integral rounded to 2 decimal places is 1.49. Show your work when computing the approximation. Report the answer...
2. Let I be the integral (a) (2 marks) Estimate I by applying the two-point Gauss-Legendre Rule once. (b) (2 marks) Estimate I by applying the two-point Gauss-Legendre Rule twice c) (2 marks) Estimate the error in your estimate for part (a). 2. Let I be the integral (a) (2 marks) Estimate I by applying the two-point Gauss-Legendre Rule once. (b) (2 marks) Estimate I by applying the two-point Gauss-Legendre Rule twice c) (2 marks) Estimate the error in your...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
3. Approximate the following integral using the two-point Gaussian quadrature rule 2 (x + a)?e(x-1)2-Bdx
Let I be the integral da x1 /2 Jo (a) (2 marks) Estimate I by applying the two-point Gauss-Legendre Rule once (b) (2 marks) Estimate I by applying the two-point Gauss-Legendre Rule twice. (c) (2 marks) Estimate the error in your estimate for part (a). Let I be the integral da x1 /2 Jo (a) (2 marks) Estimate I by applying the two-point Gauss-Legendre Rule once (b) (2 marks) Estimate I by applying the two-point Gauss-Legendre Rule twice. (c) (2...
3. (15p.) Approximate the following integral using the two-point Gaussian quadrature rule | (2 + a)*e¢8–1)-+de 2 B=1 ju a=8 0
·Using the two-point (n = 2) Gauss square method Find the value about the integral. ,(alfa and beta are both 6 ) 2 (x + a) (3-1)-B d. 0