Question

39e1/x dx, (Round your answers to six decimal places.) (a) Find the approximations T10 and M10 for T10 М10 %3 (b) Estimate the errors in the approximations of part (a). (Round your answers to six decimal places.) |EMIS (c) How large do we have to choose n so that the approximations Tn and M to the integral in part (a) are accurate to within 0.0001? for Tn n = for Mn n = Need Heln? Read It Talk to a Tutor

Answer 1

n = 10) b 2 a zl) Sol F(a) 39 e b-a oF length Divide th integval ,2] into Subintervals U-e. 15, s,1-6], (1.6, 1.7}, C1-7, 1 2), (2, 193,19, 2 and midpoinls . oS, -IS, I.2S, l.3S, I.4s, 1 SS, 1-65, f(1.)- 96. 800 S 38, f(1.2)=89. 7380 60 Now f( lo6.ol299/, FCI:3) f(1.4) 79. 6663 S6, f(I:S): 78: 961628 84. 16 6/ 16 7 70. 23 ISol, f(1.8)- 67-9734SI F(I6) 72. 861592 , f.7): f (1.9): 66- 014699 F(2)= 64.300 130 93. 0490 S8, F(1-25)26.796096 f(IS) f(oS) loi o83064, f(.yS) 77.728 098 -f(1.S5)= 74.34S484 F(1-3S) 81. Yo 20 S7 f (16S) l.494 624 F ( 1.7S ): 6 9. 06l003, fli-&S)- 66.960453 F(I.9S) 65.129797 Trapezoidal Awl (a) Tn (1n- 2 To On 2 o 106. 012991+64. 300130 800S 38 :. + 66.014699 Scanned wu 78. 85 70 So CamScalene

Now AxF(I.o Sb)J+ :.+(S1.1 ) t + O.1o1083064 t 9 3. 049 0 58 + . . + 6S =78.744974 - 39 e Now 39e x2 39 e max 39e 2x) max S I17e = k E 9r09 bound for rapezoidal E,Is k(b-a) acreb ET 17e (21i)3 = o.26 So 32 12x02 IETIS O 26 So32 fo midpoint Eron bound 24n2 IEM 7e (2-1)3 O 132S16 EMI O1325 16 Scanned with CamScanner

Fon trape zoidal Now we largl n given Choose err0% bound O. O o o K(b-a) (17e (2-1 2 1ax o.o o0 26 S o 32 48 u 18. hlS Fogr Tn n SIS fon midpoint KCb-a < D. ooo/ 1ex2хn* 11те (2-13 Q4X0.0001 364. o27 Sn Scannedith n 36S CS CamScanner