(a) Find the approximate integral of the following function using Simpson's 1/3 rule and (b) composite Simpson's 1/3 rules (use the indicated interval and the number of segments for each problem) (c) Compute also the Error of approximated integral for each problem. Lastly, (d) determine the acceptable value of ensure that the error of the method is 0.0001. if each function had to x+1 1. f(x)= x' +1 at x = [0, 3] where n = 2. f(x)= 2 at x = [0, 4] where n = 4; 3. f(x)=In(x² +2) at x = [2, 5] where n = 6; %3D sin x 4. f(x)=- 1 where n = 6; 6' 3 where n at x =| %3D | 5. f(x)=(x+1)/x at x = [0, 4] where n = 4; %3D 6. f(x)= 1+x? at x = [2, 3] where n = %3D
(a) Find the approximate integral of the following function using Simpson's 1/3 rule and (b) composite Simpson's 1/3 rules (use the indicated interval and the number of segments for each problem) (c) Compute also the Error of approximated integral for each problem. Lastly, (d) determine the acceptable value of ensure that the error of the method is 0.0001. if each function had to x+1 1. f(x)= x' +1 at x = [0, 3] where n = 2. f(x)= 2 at x = [0, 4] where n = 4; 3. f(x)=In(x² +2) at x = [2, 5] where n = 6; %3D sin x 4. f(x)=- 1 where n = 6; 6' 3 where n at x =| %3D | 5. f(x)=(x+1)/x at x = [0, 4] where n = 4; %3D 6. f(x)= 1+x? at x = [2, 3] where n = %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Number 3 and 6
![(a) Find the approximate integral of the following function using Simpson's 1/3 rule
and (b) composite Simpson's 1/3 rules (use the indicated interval and the number of
segments for each problem) (c) Compute also the Error of approximated integral for
each problem. Lastly, (d) determine the acceptable value of n if each function had to
ensure that the error of the method is 0.0001.
x+1
1. f(x)=
x? +1
at x = [0, 3] where n = 4;
2. f(x)= 2
at x = [0, 4] where n =
4;
%3D
%3D
3. f(x)= In(x² +2)
at x = [2, 5] where n = 6;
sin x
4. f(x)=
[
-] where n = 6;
at x =
6' 3
5. S(x)=(x+1)NF
at x = [0, 4] where n =
4;
6. f(x)= 1+x?
at x = [2, 3] where n = 4;
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11c4b106-15b3-40bb-a4c9-2dc56f6d01a5%2F86aaa152-b02b-4890-abe9-524f4cc644b0%2F5htshuo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Find the approximate integral of the following function using Simpson's 1/3 rule
and (b) composite Simpson's 1/3 rules (use the indicated interval and the number of
segments for each problem) (c) Compute also the Error of approximated integral for
each problem. Lastly, (d) determine the acceptable value of n if each function had to
ensure that the error of the method is 0.0001.
x+1
1. f(x)=
x? +1
at x = [0, 3] where n = 4;
2. f(x)= 2
at x = [0, 4] where n =
4;
%3D
%3D
3. f(x)= In(x² +2)
at x = [2, 5] where n = 6;
sin x
4. f(x)=
[
-] where n = 6;
at x =
6' 3
5. S(x)=(x+1)NF
at x = [0, 4] where n =
4;
6. f(x)= 1+x?
at x = [2, 3] where n = 4;
%3D
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