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In this question, you are asked to find estimates of the definite integral cos( x) dx by the Trapezoidal Rule and Simpson's Rule, each with 4 subintervals. 8.1 Firstly, in the top row below enter xo, X1, .., X4. and in the cell below each x;, enter the value of f(x;). To what accuracy, you ask? WellI, that should really depend on the error bound of the Rule, but let's say 6 decimal place accuracy, and the final answer will be accepted, if it's correct to 4 decimal places. X; in top row, f(x,) in bottom row: 8.2

In this question, you are asked to find estimates of the definite integral cos( x) dx by the Trapezoidal Rule and Simpson's Rule, each with 4 subintervals. 8.1 Firstly, in the top row below enter xo, X1, .., X4. and in the cell below each x;, enter the value of f(x;). To what accuracy, you ask? WellI, that should really depend on the error bound of the Rule, but let's say 6 decimal place accuracy, and the final answer will be accepted, if it's correct to 4 decimal places. X; in top row, f(x,) in bottom row: 8.2

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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In this question, you are asked to find estimates of the definite integral 5 cos( x ) dx 1 by the Trapezoidal Rule and Simpson's Rule, each with 4 subintervals. 8.1 Firstly, in the top row below enter x0, X1, ..., X4, and in the cell below each x;, enter the value of f(x;). To what accuracy, you ask? Well, that should really depend on the error bound of the Rule, but let's say 6 decimal place accuracy, and the final answer will be accepted, if it's correct to 4 decimal places. X; in top row, f(x;) in bottom row: 8.2 Now, give the Trapezoidal Rule estimate T4 for the value of the integral correct to 4 decimal places. T4= 8.3 Given that the maximum value of f"(x)| on the interval [1, 5] is approximately 2.223244276, what is a bound on the error ET of your answer above, to 6 decimal places. |ET| <[ 8.4 Now, give the Simpson's Rule estimate S4 for the value of the integral correct to 4 decimal places. 8.5 Given that the maximum value of |fuv)(x)| on the interval [1, 5] is approximately 23.85334968, what is a bound on the error Es of your answer above, to 6 decimal places. Es <
Transcribed Image Text:In this question, you are asked to find estimates of the definite integral 5 cos( x ) dx 1 by the Trapezoidal Rule and Simpson's Rule, each with 4 subintervals. 8.1 Firstly, in the top row below enter x0, X1, ..., X4, and in the cell below each x;, enter the value of f(x;). To what accuracy, you ask? Well, that should really depend on the error bound of the Rule, but let's say 6 decimal place accuracy, and the final answer will be accepted, if it's correct to 4 decimal places. X; in top row, f(x;) in bottom row: 8.2 Now, give the Trapezoidal Rule estimate T4 for the value of the integral correct to 4 decimal places. T4= 8.3 Given that the maximum value of f"(x)| on the interval [1, 5] is approximately 2.223244276, what is a bound on the error ET of your answer above, to 6 decimal places. |ET| <[ 8.4 Now, give the Simpson's Rule estimate S4 for the value of the integral correct to 4 decimal places. 8.5 Given that the maximum value of |fuv)(x)| on the interval [1, 5] is approximately 23.85334968, what is a bound on the error Es of your answer above, to 6 decimal places. Es <
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