(a) Find the approximations T10 M10 and $10 for [²45 4 sin(x) dx. (Round your answers to six decimal places.) 10 M10 = 510 Find the corresponding errors Ey. E and E. (Round your answers to six decimal places.) ET EM- (b) Compare the actual errors in part (a) with the error estimates found by using the smallest possible values for K in the theorem about error bounds for trapezoidal and midpoint rules and the theorem about error bound for Simpson's rule. (Round your answers to six decimal places.) |E₁| s El s El s c) Using the values of K from part (b), how large do we have to choose n so that the approximations T M and S, to the integral in part (a) are accurate to within 0.00001?
(a) Find the approximations T10 M10 and $10 for [²45 4 sin(x) dx. (Round your answers to six decimal places.) 10 M10 = 510 Find the corresponding errors Ey. E and E. (Round your answers to six decimal places.) ET EM- (b) Compare the actual errors in part (a) with the error estimates found by using the smallest possible values for K in the theorem about error bounds for trapezoidal and midpoint rules and the theorem about error bound for Simpson's rule. (Round your answers to six decimal places.) |E₁| s El s El s c) Using the values of K from part (b), how large do we have to choose n so that the approximations T M and S, to the integral in part (a) are accurate to within 0.00001?
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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Question
Transcribed Image Text:(a) Find the approximations 10
M₂0
T10
M10 NO
510
and $10 for
[²45
4 sin(x) dx. (Round your answers to six decimal places.)
Find the corresponding errors E. E. and E. (Round your answers to six decimal places.)
ET
EM "
(b) Compare the actual errors in part (a) with the error estimates found by using the smallest possible values for K in the theorem about error bounds for
trapezoidal and midpoint rules and the theorem about error bound for Simpson's rule. (Round your answers to six decimal places.)
|E₁| s
IEMI S
Eg s
(c) Using the values of K from part (b), how large do we have to choose n so that the approximations T M and S, to the integral in part (a) are accurate to
within 0.00001?
For T n
For Mn
For Sn
1009
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