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(a) Find the approximations T4 and M4 for the following integral. (Round your answers to six decimal places.) 33e1/x dx T4= 67.052465 M4 32.381044 x (b) Estimate the errors in the approximations of part (a) using the smallest possible value for K according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.) IEI ≤ 0.515625 x IEMI S 0.257813 x

(a) Find the approximations T4 and M4 for the following integral. (Round your answers to six decimal places.) 33e1/x dx T4= 67.052465 M4 32.381044 x (b) Estimate the errors in the approximations of part (a) using the smallest possible value for K according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.) IEI ≤ 0.515625 x IEMI S 0.257813 x

Advanced Engineering Mathematics
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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(a) Find the approximations T4 and M4 for the following integral. (Round your answers to six decimal places.) [²33e 33e¹/x T4 M4 67.052465 = 32.381044 X (b) Estimate the errors in the approximations of part (a) using the smallest possible value for K according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.) ET ≤ 0.515625 EM ≤ 0.257813 X (c) Using the values of K from part (b), how large do we have to choose n so that the approximations T and M to the integral in part (a) are accurate to within 0.0001? n For T, n = 474 n' dx For Mn' n = 335
Transcribed Image Text:(a) Find the approximations T4 and M4 for the following integral. (Round your answers to six decimal places.) [²33e 33e¹/x T4 M4 67.052465 = 32.381044 X (b) Estimate the errors in the approximations of part (a) using the smallest possible value for K according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.) ET ≤ 0.515625 EM ≤ 0.257813 X (c) Using the values of K from part (b), how large do we have to choose n so that the approximations T and M to the integral in part (a) are accurate to within 0.0001? n For T, n = 474 n' dx For Mn' n = 335
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