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2- Consider f (x) = e²x, and take the integral of this function over [0,1] with the following instructions: a. Use the Trapezoidal rule to approximate the integral with n = 4 subintervals. Perfom your calculations and provide the estimated integral value. b. Apply Romberg integration to improve the accuracy of your estimate. Perform at least two levels of extrapolation and discuss the results compared to the Trapezoidal rule. c. Utilize Gaussian quadrature with two points to compute the integral. Provide your calculations and compare the accuracy of this method with the previous techniques. d. Discuss the strengths and weaknesses of each numerical integration method you used in this exercise.

2- Consider f (x) = e²x, and take the integral of this function over [0,1] with the following instructions: a. Use the Trapezoidal rule to approximate the integral with n = 4 subintervals. Perfom your calculations and provide the estimated integral value. b. Apply Romberg integration to improve the accuracy of your estimate. Perform at least two levels of extrapolation and discuss the results compared to the Trapezoidal rule. c. Utilize Gaussian quadrature with two points to compute the integral. Provide your calculations and compare the accuracy of this method with the previous techniques. d. Discuss the strengths and weaknesses of each numerical integration method you used in this exercise.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2- Consider f (x) = e²x, and take the integral of this function over [0,1] with the following instructions: a. Use the Trapezoidal rule to approximate the integral with n = 4 subintervals. Perfom your calculations and provide the estimated integral value. b. Apply Romberg integration to improve the accuracy of your estimate. Perform at least two levels of extrapolation and discuss the results compared to the Trapezoidal rule. c. Utilize Gaussian quadrature with two points to compute the integral. Provide your calculations and compare the accuracy of this method with the previous techniques. d. Discuss the strengths and weaknesses of each numerical integration method you used in this exercise.
Transcribed Image Text:2- Consider f (x) = e²x, and take the integral of this function over [0,1] with the following instructions: a. Use the Trapezoidal rule to approximate the integral with n = 4 subintervals. Perfom your calculations and provide the estimated integral value. b. Apply Romberg integration to improve the accuracy of your estimate. Perform at least two levels of extrapolation and discuss the results compared to the Trapezoidal rule. c. Utilize Gaussian quadrature with two points to compute the integral. Provide your calculations and compare the accuracy of this method with the previous techniques. d. Discuss the strengths and weaknesses of each numerical integration method you used in this exercise.
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