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In this question, you are asked to find estimates of the definite integral 12 sin( x² ) 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 vahue of fix,). 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, fix,) in bottom row: 8.2 Now, give the Trapezoidal Rule estimate T, for the value of the integral correct to 4 decimal places.

In this question, you are asked to find estimates of the definite integral 12 sin( x² ) 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 vahue of fix,). 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, fix,) in bottom row: 8.2 Now, give the Trapezoidal Rule estimate T, for the value of the integral correct to 4 decimal places.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In this question, you are asked to find estimates of the definite integral sin( 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? 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, fix,) in bottom row: 8.2 Now, give the Trapezoidal Rule estimate T, for the value of the integral correct to 4 decimal places. 8.3 Given that the maximum value of f'(x) on the interval [0, 1/2] is approximately 2, what is a bound on the error ET of your answer above, to 6 decimal places. 8.4 Now, give the Simpson's Rule estimate Sa for the value of the integral correct to 4 decimal places. 8.5 Given that the maximum value of f(x) on the interval [0, 1/2] is approximately 14.34839261, what is a bound on the error Es of your answer above, to 6 decimal places. Es s
Transcribed Image Text:In this question, you are asked to find estimates of the definite integral sin( 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? 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, fix,) in bottom row: 8.2 Now, give the Trapezoidal Rule estimate T, for the value of the integral correct to 4 decimal places. 8.3 Given that the maximum value of f'(x) on the interval [0, 1/2] is approximately 2, what is a bound on the error ET of your answer above, to 6 decimal places. 8.4 Now, give the Simpson's Rule estimate Sa for the value of the integral correct to 4 decimal places. 8.5 Given that the maximum value of f(x) on the interval [0, 1/2] is approximately 14.34839261, what is a bound on the error Es of your answer above, to 6 decimal places. Es s
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