The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. X 0 sin tdt Ta (Round to four decimal places as needed.) An upper bound for Er is (Round to four decimal places as needed.) b. Evaluate the integral directly and find |ET| A S 0 (Type an exact answer in simplified form.) sin dt = ..... |ET|= (Round to four decimal places as needed.). c. Use the formula (|ET|/(true value)) x 100 to express |ET| as a percentage of the integral's true value. (Round to one decimal place as needed.)
The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. X 0 sin tdt Ta (Round to four decimal places as needed.) An upper bound for Er is (Round to four decimal places as needed.) b. Evaluate the integral directly and find |ET| A S 0 (Type an exact answer in simplified form.) sin dt = ..... |ET|= (Round to four decimal places as needed.). c. Use the formula (|ET|/(true value)) x 100 to express |ET| as a percentage of the integral's true value. (Round to one decimal place as needed.)
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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Question
Transcribed Image Text:The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts.
X
0
I
sin tdt
T≈
(Round to four decimal places as needed.)
An upper bound for E is
(Round to four decimal places as needed.)
b. Evaluate the integral directly and find |ET|-
sin dt = 2
...
(Type an exact answer in simplified form.)
|ET|=0
(Round to four decimal places as needed.)
c. Use the formula (|ET|/(true value)) x 100 to express |ET| as a percentage of the integral's true value.
%
(Round to one decimal place as needed.)
Transcribed Image Text:The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts.
X
sin tdt
(Round to one decimal place as needed.)
II. Using Simpson's rule complete the following.
a. Estimate the integral with n=4 steps and find an upper bound for Es
S≈
(Round to four decimal places as needed.)
An upper bound for Es is
(Round to four decimal places as needed.)
b. Using the value of the integral found by evaluating directly in part 1.b., find Es
Es
(Round to four decimal places as needed.)
c. Use the formula (Es/(true value)) x 100 to express |Es as a percentage of the integral's true value.
%
(Round to one decimal place as needed.)
Expert Solution
Step 1: Evaluation of integral by using trapezoidal rule:
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