X y 0 1 You need to find the value of the integral f(x) dx where the following data is available: 1 0.0156 2 0.0029 0.5 0.064 1.5 0.006 a) Use multiple applications of the trapezoid rule. b) Apply the composite trapezoid rule. 2.5 0.0016 3 0.001
X y 0 1 You need to find the value of the integral f(x) dx where the following data is available: 1 0.0156 2 0.0029 0.5 0.064 1.5 0.006 a) Use multiple applications of the trapezoid rule. b) Apply the composite trapezoid rule. 2.5 0.0016 3 0.001
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
![You need to find the value of the integral:
\[
\int_{0}^{3} f(x) \, dx
\]
where the following data is available:
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 \\
\hline
y & 1 & 0.064 & 0.0156 & 0.006 & 0.0029 & 0.0016 & 0.001 \\
\hline
\end{array}
\]
a) Use multiple applications of the trapezoid rule.
b) Apply the composite trapezoid rule.
c) Use multiple applications of Simpson’s 1/3 rule.
d) Apply the composite Simpson’s 1/3 rule.
e) Use multiple applications of Simpson’s 3/8 rule.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F140bd83b-645e-45c3-8644-e53276eab044%2F5c030aa5-5125-484a-a9ed-9877f02a3e7f%2Fohoos96_processed.png&w=3840&q=75)
Transcribed Image Text:You need to find the value of the integral:
\[
\int_{0}^{3} f(x) \, dx
\]
where the following data is available:
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 \\
\hline
y & 1 & 0.064 & 0.0156 & 0.006 & 0.0029 & 0.0016 & 0.001 \\
\hline
\end{array}
\]
a) Use multiple applications of the trapezoid rule.
b) Apply the composite trapezoid rule.
c) Use multiple applications of Simpson’s 1/3 rule.
d) Apply the composite Simpson’s 1/3 rule.
e) Use multiple applications of Simpson’s 3/8 rule.
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