(a) Find the approximations T₁0, M10 and $10 for 4 34 sin(x) dx. (Round your answers to six decimal places.) T10 = Mio $10 - Find the corresponding errors E, EM, and E. (Round your answers to six decimal places.) ET= EM = Es = (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.) IE, S IEMI S Egl s (c) Using the values of K from part (b), how large do we have to choose n so that the approximations TM and S, to the integral in part (a) are accurate to within 0.00001? For T n= For Mn = For Sn, n =
(a) Find the approximations T₁0, M10 and $10 for 4 34 sin(x) dx. (Round your answers to six decimal places.) T10 = Mio $10 - Find the corresponding errors E, EM, and E. (Round your answers to six decimal places.) ET= EM = Es = (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.) IE, S IEMI S Egl s (c) Using the values of K from part (b), how large do we have to choose n so that the approximations TM and S, to the integral in part (a) are accurate to within 0.00001? For T n= For Mn = For Sn, n =
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
Answer the both Qesion ASAP.
Transcribed Image Text:(a) Find the approximations T10, M10'
T10
M10
S10
=
=
=
=
Find the corresponding errors ET, EM, and E. (Round your answers to six decimal places.)
ET
EM =
ем
Es
=
π
6.²
34 sin(x) dx. (Round your answers to six decimal places.)
|E| ≤
IEMI ≤
Esl ≤
M10, and S₁ for
10
(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.)
For Sn, n =
'n'
(c) Using the values of K from part (b), how large do we have to choose n so that the approximations TM and Sn to the integral in part (a) are accurate to within 0.00001?
n'
For T₁, n =
For M₁, n =
'n'
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