(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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 81E
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Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3361ca50-fe39-4902-8c9b-25c25195dd96%2Ff05087cd-7072-466c-9b1e-45f94f8e9499%2Fek6ne5_processed.jpeg&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3361ca50-fe39-4902-8c9b-25c25195dd96%2Ff05087cd-7072-466c-9b1e-45f94f8e9499%2F53su6p8_processed.jpeg&w=3840&q=75)
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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