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ma101-203mt2sol - 1 Evaluate these integrals(a...

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Unformatted text preview: 1. Evaluate these integrals: (a) fxsin(2m)dzn. .— [4} (b) [0132mdx Wait; Xx" W59 W). ' 1 ; wee" :.: IMQ t‘flfiztfgéfla #36?ng Am - 0 :fN/Q]..405o29 {4.405929% 2:9? m 9‘ ‘9‘ 1 1T3. fill 2 .- [+Qé4g 3-,— 1., 40% 29M; :17: I ( 1 flg ‘f 0 I 'fT/L ‘ééadgg 7 :M [“COS " Inswel‘ 8S A 1/3. “IT/[G :é—[gflrflé’] r-W/é ' ’1‘ 0 2. Evaluate these integrals: 3 5 [4] (a) [tan3ase63d9 2::— [“2” 1 2L, +C ;: 47M 9 “PC 3 3 Mu:+mé9 Mzaecéwwé (it [4] (b) / (t -— 1m: ~41) [4] [4] {4] 3. Determim convergence of these improper integrais and expiain your answer. (*1)/Uoom3:1d$ 3': M if!” 4 J" 5) 23:71 211+7x X 00 MW/fl WW$C+Pi)/M% E3 40 fl; MW mmyfis (WWW) % ”Sf 3+ 151 wer X ( 60A} Vflgéym 56 @4456 0 B W» W) 9% 7 W 0 wNME/EG WW5 Up 4. mm ”4:23 [4] 4. Using the IVIaclanrin series expemsion of (am in powers of 35... . . . . ,3 .2 (35) Give the first five terms of the senes for j e ‘1 da: -1 5. We wish to estimate / cos(:r3)da: using the 'l‘rapezeidal rule. . 0 (a) Calculate the trapezoidal estimate, using four equal subintervals (do not simplify): _ x F _- ‘1‘ h J H i, m)" I m. '3‘ ”N f.‘ Urn-“m. f”. "(1.; (I I ,1" :73: , It.“ / , r 5' ‘, '{j‘a 'f"’j"i’ 7 J 3’ 2- ”7’3 1W < {rift 'I’“'</57//) 'f 2 mi? "'73) -+ J 65%) J l. (b) Show that if fix) : eos(:c_3) then ~15 g f”(:t') < 0 for O S a: S 1 «Kg. -\ “-- L1)”, term . K/ . ta hrs ‘ K J ./ fr! X 2. .’ 4 f. wweaxjawflwwvs _J (c) Is the trapezoidal estimate an overestimate or underestimate? Explain. // ./}"' I ,_ '5‘ ‘J' , ,. :13; 3 ._ , ‘ , _ :2 4-1., j’lé'gftgflyfl. g. ( . > (1/, H (I. (7.,- gqm J (K gig.- jL it z." W 1 wig. .g » ’ __ '3 ((1) Using the trapezoidal error estimate ierrerl S #27231, where if”(:c)| S K for an in [(1,1)]. how big must it be to ensure the error in the trapezoidal estimate is at most 0.01? (i ...
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