Given. [² 35 cos(x²) dx Do the following. (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8= 31.581649 Mg = 31.6967 (b) Estimate the errors in the approximations Tg and Mg in part (a). (Use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error. Round your answer to seven decimal places.) IETI ≤ 0.2734375 IEMI ≤ 0.1367188 (c) How large do we have to choose n so that the approximations Tn and Mn to the integral are accurate to within 0.0001? (Use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error.) nz X for T nz X for Mn

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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question (c), and for Tn, it is not 418
Given.
²35
35 cos(x²) dx
Do the following.
(a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.)
T8 31.581649
Mg = 31.6967
(b) Estimate the errors in the approximations Tg and Mg in part (a). (Use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error. Round
your answer to seven decimal places.)
IETIS 0.2734375
IEMI ≤ 0.1367188
(c) How large do we have to choose n so that the approximations Tn and Mn to the integral are accurate to within 0.0001? (Use the fact that the range of the sine and cosine functions is
bounded by ±1 to estimate the maximum error.)
nz
X for T
ΠΣ
X for M
Transcribed Image Text:Given. ²35 35 cos(x²) dx Do the following. (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 31.581649 Mg = 31.6967 (b) Estimate the errors in the approximations Tg and Mg in part (a). (Use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error. Round your answer to seven decimal places.) IETIS 0.2734375 IEMI ≤ 0.1367188 (c) How large do we have to choose n so that the approximations Tn and Mn to the integral are accurate to within 0.0001? (Use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error.) nz X for T ΠΣ X for M
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