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/2 -x/2 2 costdt 1. Using the trapezoidal rule complete the following a. Estimate the integral with n=4 steps and find an upper bound for E- T=0 (Simplify your answer. Round to four decimal places as needed) An upper bound for Eis (Round to four decimal places as needed.) b. Evaluate the integral directly and find Er */2 2 cos dt = - 1/2 (Type an integer or a decimal) |E|-0 (Simplify your answer. Round to four decimal places as needed) c. Use the formula (Er(true value)) x 100 to express |E₁| as a percentage of the integral's true value. (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= (Simplify your answer. Round to four decimal places as needed.) An upper bound for Es is (Round to four decimal places as needed.) b. Evaluate the integral directly and find Es n/2 S 2 cos dt = -8/2 (Type an integer or a decimal) (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.)
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/2 -x/2 2 costdt 1. Using the trapezoidal rule complete the following a. Estimate the integral with n=4 steps and find an upper bound for E- T=0 (Simplify your answer. Round to four decimal places as needed) An upper bound for Eis (Round to four decimal places as needed.) b. Evaluate the integral directly and find Er */2 2 cos dt = - 1/2 (Type an integer or a decimal) |E|-0 (Simplify your answer. Round to four decimal places as needed) c. Use the formula (Er(true value)) x 100 to express |E₁| as a percentage of the integral's true value. (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= (Simplify your answer. Round to four decimal places as needed.) An upper bound for Es is (Round to four decimal places as needed.) b. Evaluate the integral directly and find Es n/2 S 2 cos dt = -8/2 (Type an integer or a decimal) (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.)
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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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/2
<-x/2
2 costdt
1. Using the trapezoidal rule complete the following
a. Estimate the integral with n=4 steps and find an upper bound for E-
T=0
(Simplify your answer. Round to four decimal places as needed.)
An upper bound for Eis
(Round to four decimal places as needed)
b. Evaluate the integral directly and find Er
*/2
2 co
2 cos dt =
- 1/2
(Type an integer or a decimal)
(Simplify your answer. Round to four decimal places as needed)
c. Use the formula (E+/(true value)) x 100 to express |E| as a percentage of the integral's true value.
(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=
(Simplify your answer. Round to four decimal places as needed.)
An upper bound for Es is
(Round to four decimal places as needed.)
b. Evaluate the integral directly and find Es
n/2
S 2 cos dt =
-1/2
(Type an integer or a decimal)
(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.).
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