Question

5." 9 sin(x) dx. (Round your answers to six decimal places.) (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.) Els IEM Esls (c) 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? n= for T. for Me for Sn n= n= Need Help? Read It Watch It Talk to a Tutor

Answer 1

a). Let ya fea) = 9 Sin (2) " ftuar = lo "9 Sin (a) dx . 0 /-O 7-10 h: 70 n. 10, > a X > 0,62 X10 xotih = 0+ ixit 70 70 į 6 O 1 3 4 5 7 9 xe 0 2170317/10 4% 51% GP70 710 3/10 9", Yir I Sino Mb9016 5.290, 7:231 8:559 9 8:559 7.281 5:290 778) 2.7812529 0672 1529 5086 5086 1522 0672 1519 Tho '%) © By Trapezoider Ruk: 9 din[alda - To = ķi / %+40 + 9 (9,* **** [0+ 0+0+2 (2.781 252 9 +512900672 +7.2811529 2 X Ett 2 10 + 8.559 5086 + 712811529 + 8.559 508 6 + 9 7 5:290067 2 + 2.7811529 lorox/2x9f El. T 2 10 41278/25297 5.290 0672 + 7•2811529 + 8-559 5085)] 17-851774 (Rounded up to 6-decimal places) I Tio (Regd.) + franaray] > By sled point formula, (1) J I sin(x) dx ~ Mio = h. [ f(repe) + freque) + frete) +... = f ( f) if (300+ f (T) + f ( t) + f ( 9 )+7(497) f(199) + f(159) + f(177)+ f(120)] 11

91T IIT TT los Sin! 40 + 9 Sin I sin 31 2 +9 sin St to + 9 Sin to you t + 9 Sin 12:17 15T + I sin 177 +Isin f I sin 20 13T 20 9 sin +9 sing i sin (0-8) 20 20 A [9 sin 17 it 9 Sin 37 + 9 Soin 5 + 9-son? + 9 Bin (-3) + 9 &in (n - 35 ) +980(7- + 9 Sin (11-36) a line I sin(n-12-20) Sindri T ܘܐ [2x9 (sin + toimega + din+ 13"[0:15643840. 453 9964 + 01 707 106.3 + 0-891 0365+ 09976293 (Rounded up to six decimal places.) 18.074 235 Readi T Josidopaz S-10 0 salm Ho 0+ 0 40 +9 Sin Git 917 2 •sin + 70 By Sympson's å rules $ / % +7 %+%+4(94734 Yout >>#99) +2 (7,4%,**)] 4(98ing met Olin To + gSin z. o r g Sin +9 297 +9 (gain 7+9 Sins to sin st) + sin Rinze + Sin ) +18 (din zot rein we ons + sin some + sin $)) o [36x (3.236 0680) +18 (3.079 6835) ] C Rounded up to I six decimal places) colla [ & sin 315 (sin 36 10 11 30 .: Sro = 18.000 986 (Read)

IT # Exact cadae Value of ! 9 Sin (a)dx - 91632]." - 9 (631-60) -9-1-1) 18 | To Exact value / Eq . 17.851 774-18/ (Rounded up to 6. decimal places) Er E 0 148 226 (Read) / Mio Exact value/ 2 E EM 1 18.074235 -181 0.074 235 Cread.) 1. Ens Es = | Sco- Exact Vale/ - 18.000 986-18) 0 000 986 Riegdi Es

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