26 sin(x) dx. (Round your answers to six decimal places.) Jo (a) Find the approximations T. 10 M10 and S,0 for T10 = 51.571612 M10 52 214458 %3D S10 = 52.002847 Find the corresponding errors E, E, and Es. (Round your answers to six decimal places.) = 0.428388 ET EM -0.214458 %3D Es -0.002847 %3D (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.) IEI S 0 671802 IE s 0.335901 IE s 0.004420 (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 Tn=1988 For n1406 M For Sn=41 x x x

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
(a) Find the approximations T
26 sin(x) dx. (Round your answers to six decimal places.)
10 "10 and S,, for
= 51.571612
T30
M10
52.214458
= 52.002847
S10
Find the corresponding errors E, E and Es (Round your answers to six decimal places.)
ET
= 0.428388
EM
-0.214458
%3D
Es
-0.002847
%3D
(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.)
IEI s 0 671802
IE S 0.335901
IEg s 0004420
(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 0.000012
For Tn=1988
For Mn= 1406
For Sn-41
X >>
>>
Transcribed Image Text:(a) Find the approximations T 26 sin(x) dx. (Round your answers to six decimal places.) 10 "10 and S,, for = 51.571612 T30 M10 52.214458 = 52.002847 S10 Find the corresponding errors E, E and Es (Round your answers to six decimal places.) ET = 0.428388 EM -0.214458 %3D Es -0.002847 %3D (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.) IEI s 0 671802 IE S 0.335901 IEg s 0004420 (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 0.000012 For Tn=1988 For Mn= 1406 For Sn-41 X >> >>
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