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(Numerical Integration: Composite Rectangle Rule). All numerical answers should be rounded to 8-digit floating-point numbers. (i) (a) Use the Composite Rectangle Rule with n = 20 to find an approximation I* of the integral In(40.8+ sin² (x)) dx (b) Show your work by filling in the following table of selected values of the grid points and the values of the integrand at these points: k 0 5 10 15 19 Xk 0.5 I = Yk

(Numerical Integration: Composite Rectangle Rule). All numerical answers should be rounded to 8-digit floating-point numbers. (i) (a) Use the Composite Rectangle Rule with n = 20 to find an approximation I* of the integral In(40.8+ sin² (x)) dx (b) Show your work by filling in the following table of selected values of the grid points and the values of the integrand at these points: k 0 5 10 15 19 Xk 0.5 I = Yk

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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Numerical Analysis and Its Applications.
(Numerical Integration: Composite Rectangle Rule). All numerical answers should be rounded to 8-digit floating-point numbers. (i) (a) Use the Composite Rectangle Rule with n - integral 5 10 In(40.8+ sin² (x)) dx (b) Show your work by filling in the following table of selected values of the grid points and the values of the integrand at these points: k 0 15 19 Xk I 0.5 = So 20 to find an approximation I* of the Yk
Transcribed Image Text:(Numerical Integration: Composite Rectangle Rule). All numerical answers should be rounded to 8-digit floating-point numbers. (i) (a) Use the Composite Rectangle Rule with n - integral 5 10 In(40.8+ sin² (x)) dx (b) Show your work by filling in the following table of selected values of the grid points and the values of the integrand at these points: k 0 15 19 Xk I 0.5 = So 20 to find an approximation I* of the Yk
(ii) By (1), I* = In this and the following problems, it is a good idea to obtain a sufficiently accurate approximation of the integral in question by executing the commands similar to evalf( integral (f (x), x = a.. b), 14 ) or to N[ Integrate [ f [x], {x,a, b}], 14 ] at the Wolfram Alpha website, or any other online resource/software, in order to compare with your answer. Check
Transcribed Image Text:(ii) By (1), I* = In this and the following problems, it is a good idea to obtain a sufficiently accurate approximation of the integral in question by executing the commands similar to evalf( integral (f (x), x = a.. b), 14 ) or to N[ Integrate [ f [x], {x,a, b}], 14 ] at the Wolfram Alpha website, or any other online resource/software, in order to compare with your answer. Check
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