(a) Find the approximations T10, M10, and S10 for T10= M10= S10= Find the corresponding errors ET, EM, and Es. (Round your answers to six decimal places.) ET= EM = Es= (b) Compare the actual errors in part (a) with the error estimates given by 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.) |ET| S EMIS |Esl s S." 40 sin x dx. (Round your answers to six decimal places.) (c) How large do we have to choose n so that the approximations Tn, Mn, and S, to the integral in part (a) are accurate to within 0.00001? for Tn for Mn for Sn n= n= n=
(a) Find the approximations T10, M10, and S10 for T10= M10= S10= Find the corresponding errors ET, EM, and Es. (Round your answers to six decimal places.) ET= EM = Es= (b) Compare the actual errors in part (a) with the error estimates given by 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.) |ET| S EMIS |Esl s S." 40 sin x dx. (Round your answers to six decimal places.) (c) How large do we have to choose n so that the approximations Tn, Mn, and S, to the integral in part (a) are accurate to within 0.00001? for Tn for Mn for Sn n= n= 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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Transcribed Image Text:"π
(a) Find the approximations T10, M10, and S10 for
S."
40 sin x dx. (Round your answers to six decimal places.)
T10 =
M10 =
S10=
Find the corresponding errors ET, EM, and Es. (Round your answers to six decimal places.)
ET =
EM =
Es =
(b) Compare the actual errors in part (a) with the error estimates given by 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.)
|ET| ≤
|EMI ≤
|Esl ≤
(c) How large do we have to choose n so that the approximations T, Mn, and S, to the integral in part (a) are accurate to within 0.00001?
n =
for Tn
for Mn
for Sn
n =
n =
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