Evaluate ∫1 9 7/s^2 ds using the trapezoidal rule and Simpson's rule. Determine i. the value of the integral directly. ii. the trapezoidal rule estimate for n = 4. iii. an upper bound for |ET|. iv. the upper bound for |ET| as a percentage of the integral's true value. v. the Simpson's rule estimate for n = 4. vi. an upper bound for |ES|. vii. the upper bound for |ES| as a percentage of the integral's true value. The value of ∫1 s 9 7/s^2 ds is (Round to four decimal places as needed.) The trapezoidal rule estimate of ∫1 9 7/s^2 ds for n = 4 is (Round to four decimal places as needed.) The upper bound on |ET | is (Round to four decimal places as needed.) The upper bound for |ET| as a percentage of the integral's true value is (Round to four decimal places as needed.) The Simpson's rule estimate of ∫1 9 7/s^2 ds for n = 4 is (Round to four decimal places as needed.) The upper bound on |ES| is (Round to four decimal places as needed.) The upper bound for |ES| as a percentage of the integral's true value is (Round to four decimal places as needed.)
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Evaluate ∫1 9 7/s^2 ds using the trapezoidal rule and Simpson's rule. Determine i. the value of the integral directly. ii. the trapezoidal rule estimate for n = 4. iii. an upper bound for |ET|. iv. the upper bound for |ET| as a percentage of the integral's true value. v. the Simpson's rule estimate for n = 4. vi. an upper bound for |ES|. vii. the upper bound for |ES| as a percentage of the integral's true value. The value of ∫1 s 9 7/s^2 ds is (Round to four decimal places as needed.) The trapezoidal rule estimate of ∫1 9 7/s^2 ds for n = 4 is (Round to four decimal places as needed.) The upper bound on |ET | is (Round to four decimal places as needed.) The upper bound for |ET| as a percentage of the integral's true value is (Round to four decimal places as needed.) The Simpson's rule estimate of ∫1 9 7/s^2 ds for n = 4 is (Round to four decimal places as needed.) The upper bound on |ES| is (Round to four decimal places as needed.) The upper bound for |ES| as a percentage of the integral's true value is (Round to four decimal places as needed.)
![The sine-integral function, shown below, is one of the many functions in engineering whose formulas cannot be simplified. There is no elementary formula for the antiderivative of (sin t)/t. Complete parts (a) through (c) below. Si(x) = ∫x 0 sint/t dt 1 Click the icon to view more information. a. Use the fact that |f^(4)| ≤ 1 on [0, π/2] to give an upper bound for the error that will occur if Si (π/2) = ∫0 π/2 sint/t dt is estimated by Simpson's Rule with n = 4. (Round to five decimal places as needed.) b. Estimate Si (π/2) by Simpson's Rule with n = 4. (Round to five decimal places as needed.) c. Express the error bound you found in part (a) as a percentage of the value you found in part (b). % (Round to three decimal places as needed.)](https://www.doubtrix.com/js/ckeditor/filemanager/connectors/php/editor/1701534945-nxzgazgdj.png)