The table lists several measurements gathered in an experiment to approximate an unknown continuous function y = f(x). X 0.00 0.50 0.75 1.00 1.50 1.75 2.00 y 4.24 4.77 5.48 6.30 7.83 8.28 8.35 (a) Can you use the Trapezoidal Rule to approximate the integral f(x) dx? Why or why not? O. No; the intervals are not of equal width. O Yes; the function is continuous. No; the concavity of the function changes. O Yes; the Trapezoidal Rule can be used to approximate any integral. (b) Approximate the integral 1² using the Trapezoidal Rule or a trapezoidal sum. (Round your answer to three decimal places.) f(x) dx
The table lists several measurements gathered in an experiment to approximate an unknown continuous function y = f(x). X 0.00 0.50 0.75 1.00 1.50 1.75 2.00 y 4.24 4.77 5.48 6.30 7.83 8.28 8.35 (a) Can you use the Trapezoidal Rule to approximate the integral f(x) dx? Why or why not? O. No; the intervals are not of equal width. O Yes; the function is continuous. No; the concavity of the function changes. O Yes; the Trapezoidal Rule can be used to approximate any integral. (b) Approximate the integral 1² using the Trapezoidal Rule or a trapezoidal sum. (Round your answer to three decimal places.) f(x) dx
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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![The table lists several measurements gathered in an experiment to approximate an unknown continuous function \( y = f(x) \).
\[
\begin{array}{c|c|c|c|c|c|c}
x & 0.00 & 0.50 & 0.75 & 1.00 & 1.50 & 1.75 & 2.00 \\
\hline
y & 4.24 & 4.77 & 5.48 & 6.30 & 7.83 & 8.28 & 8.35 \\
\end{array}
\]
(a) Can you use the Trapezoidal Rule to approximate the integral \(\int_{0}^{2} f(x) \, dx\)? Why or why not?
- ○ No; the intervals are not of equal width.
- ○ Yes; the function is continuous.
- ○ No; the concavity of the function changes.
- ○ Yes; the Trapezoidal Rule can be used to approximate any integral.
(b) Approximate the integral \(\int_{0}^{2} f(x) \, dx\) using the Trapezoidal Rule or a trapezoidal sum. (Round your answer to three decimal places.)
\(\boxed{} \)
(c) Use a graphing utility to find a model of the form \( y = ax^3 + bx^2 + cx + d \) for the data. (Round your coefficients to four decimal places.)
\( y = \boxed{} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa89fcfbc-9661-4037-a401-8de41697cbc3%2Fadb1f194-7c66-4eda-b05e-e26fbc6f830b%2Fc8j8zq8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The table lists several measurements gathered in an experiment to approximate an unknown continuous function \( y = f(x) \).
\[
\begin{array}{c|c|c|c|c|c|c}
x & 0.00 & 0.50 & 0.75 & 1.00 & 1.50 & 1.75 & 2.00 \\
\hline
y & 4.24 & 4.77 & 5.48 & 6.30 & 7.83 & 8.28 & 8.35 \\
\end{array}
\]
(a) Can you use the Trapezoidal Rule to approximate the integral \(\int_{0}^{2} f(x) \, dx\)? Why or why not?
- ○ No; the intervals are not of equal width.
- ○ Yes; the function is continuous.
- ○ No; the concavity of the function changes.
- ○ Yes; the Trapezoidal Rule can be used to approximate any integral.
(b) Approximate the integral \(\int_{0}^{2} f(x) \, dx\) using the Trapezoidal Rule or a trapezoidal sum. (Round your answer to three decimal places.)
\(\boxed{} \)
(c) Use a graphing utility to find a model of the form \( y = ax^3 + bx^2 + cx + d \) for the data. (Round your coefficients to four decimal places.)
\( y = \boxed{} \)
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