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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Transcribed Image Text: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
[²
(a) Can you use the Trapezoidal Rule to approximate the integral
O. No; the intervals are not of equal width.
O Yes; the function is continuous.
O No; the concavity of the function changes.
O Yes; the Trapezoidal Rule can be used to approximate any integral.
(b) Approximate the integral
f(x) dx
y =
f(x) dx? Why or why not?
using the Trapezoidal Rule or a trapezoidal sum. (Round your answer to three decimal places.)
(c) Use a graphing utility to find a model of the form
y = ax³ + bx² + cx + d
for the data. (Round your coefficients to four decimal places.)
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