Question

% 2.2.27 Certain indefinite integrals such as ex dx cannot be expressed in finite terms using elementary functions. When such an integral is encou Simpson's rule with n = 4 to approximate an answer to part b at x = 0.5 to three decimal places. Click the icon to view an example of this process. a. Solve the initial value problem sex with y(0) = 2. Use t as the variable of integration in the explicit solution. b. Solve the initial value proble = ex y-2, with y(0) = 1. Use t as the variable of integration in the explicit solution c. Solve the initial value prob V3+ sin x (1 + y2), with y(0) = 1. Use t as the variable of integration in the explicit solution. d. Use Simpson's rule with n = 4 to approximate the solution to part b at x = 0.5 to three decimal places. Click the icon to review Simpson's rule. y(0.5) - 1.381 (Round to three decimal places as needed.)

Answer 1

Answer Given that i- a) and globzo → Indegrading both sides under the limits JL=0 to do, we get > you see the → 964.) = 0 = 8.42X de - ~ Now bay taking t as the variable of integration and replacing on by se, we get

b) Here the deel?, g2, is(o)=1 → Integrading both sides within limits . xco do so, we get → Sos od day parang ada de ano => } [296,33?,] - entire → by replacing te by x and taking the 2 as the radicables of integration, we get the one

༧ c) Here the day y = Jitsina (1+eg?), "9/0)=1 མེད ། ད བན ཅ ཆ ་ན། དང ་ ། ༽ དག བཅུ FRPན ༣ both s༣ ན བ &iPh། |:ཀ༥52༢ ཅེང -༤ :༠ ན་ ， &c sgE > ཅིང༌ ༢ ༣ ན་ 1: ཅུང་ dan tag (1) - dan 'y(o) = Jitsin xdur -> > ནས་ ༥ (༥) – བོད > དཀ ། ང ་ ་ བ ང་རྒྱལ། ཆབ་ཆུང ཅ ༌ ༧/ - Replacing di by a and taking 't'as the variable of intestation, we ged dany (K) = 1 + Sitsindad E ཀུ། | +9 བྱེ་བྱ [ $)

d) Here the lewe have > YW = {32 latti? - o n - 460)=1 → Now the we have to find the appoose solution at d = o.5 by using simpson's rule. So we divide the inderval o to oes into Even number Parts Chat is subintervals). for the fu f(x) = f* et al Flu) to l 0.125 0.25 e-125 e 25 0. 375 0.5 e.315 .5 pos flx) &x= 0.125 56 (0)14(8 (+125) + f (0-375)) 12 (860-25+7(0-3)

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