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Answer: Trapezoid Rule and Simpson’s Rule Consider the
Chapter 5, Problem 33E(choose chapter or problem)
Trapezoid Rule and Simpson's Rule Consider the following integrals and the given values of n.
(a) Find the Trapezoid Rule approximations to the integral using n and 2n subintervals.
(b) Find the Simpson's Rule approximation to the integral using 2n subintervals. It is easiest to obtain Simpson's Rule approximations from the Trapezoid Rule approximations, as in Example 6.
(c) Compute the absolute errors in the Trapezoid Rule and Simpson's Rule with 2n subintervals.
\(\int_{1}^{e} \frac{1}{x} d x\) ; n=50
Questions & Answers
QUESTION:
Trapezoid Rule and Simpson's Rule Consider the following integrals and the given values of n.
(a) Find the Trapezoid Rule approximations to the integral using n and 2n subintervals.
(b) Find the Simpson's Rule approximation to the integral using 2n subintervals. It is easiest to obtain Simpson's Rule approximations from the Trapezoid Rule approximations, as in Example 6.
(c) Compute the absolute errors in the Trapezoid Rule and Simpson's Rule with 2n subintervals.
\(\int_{1}^{e} \frac{1}{x} d x\) ; n=50
ANSWER:Step 1 of 5
Given integral is
(a) Trapezoidal rule states that
We have that a=1, b=?, n=50.
Therefore
Divide interval [1, inti n=50 subintervals of length
with the following endpoints a=1,