Class Activity 2 Evaluate the following integral using 3 point Gauss quadrature. sin/x) dx Answer: I 0.6681
evalu
1. Evaluate 52 dx by using composite midpoint method with n-1 to approximate the definite integral. (25 points, credits are given based on your calculation procedure) м.cro ,,4 2 1+23 2 2. Evaluate 1 -S Se-23 dy by using Gauss quadrature with two Gauss points. (25 points, credits are given based on your calculation procedure) (hints: weight coefficient and Gauss points Coordinates are on the last page) 0.1 2. 3. Use Euler's explicit method to solve the ordinary differential...
Using a two-point Gauss quadrature, where the weights and abscissae are provided in the table i Si 1 1.0 IS 2 1.0 the value of the integral is estimated to be 5.54 5.78 None of the above. 5.67 5.69
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
1. Use the Gauss two-point quadrature rule to approximate and compare the result with the trapezoidal and Simpson rules.
1. Use the Gauss two-point quadrature rule to approximate and compare the result with the trapezoidal and Simpson rules.
1. (Program) Evaluate f e dr using the rectangle rule (mid-point rule), the trapezoid rule, and the two-point Gauss quadrature rule with various values of Ar. Since the error estimates have the form ElCAr" you should be able to computationally verify them by observing log El logC +plogAr and plotting log|E versus logAr to estimate p.
1. (Program) Evaluate f e dr using the rectangle rule (mid-point rule), the trapezoid rule, and the two-point Gauss quadrature rule with various values...
- Sox using with 2,4, and equal o Evaluate the integral i) Composite trapezoidal rub, () composite simpsunds rule sub infortals. y Evaluate the integral Subdividing the interval parts and then applying three pant formula. I=s dx by to, i] into two equal the Gauss Legentre • Ttx i tx 1a) Evaluate the Integral I= ĵ dx using i) Composite trapezoidal ic Composite Simpson rule sub intervals rule si into 2,4 and 8 3) Evaluate the integral I = I...
Numerical Analysis:
a) The basic form of the Gaussian quadrature formula is The integration formula using two points can be made exact when a polynomial of order 3 is integrated. i) Determine the weights c, c2 and the points , 2 e-radz.16] (ii) By find using a change of variable use Gaussian Quadrature to 0
a) The basic form of the Gaussian quadrature formula is The integration formula using two points can be made exact when a polynomial of order...
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.
A weighted Gauss quadrature formula for the weight function
is
(a) The formula is exact for
, what is
?
(b) Use this formula to approximate the integral (keep 9 decimal
places)
.
(c) Compute the error. (Note: The error is less than
.)
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