Question

4 Compare these results with the approximation of the Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with integral using a graphing utility. (Round your answers to four decimal places.) 1/2 sin(x) dx Trapezoidal Simpson's graphing utility Need Help? Read Watch T alk to a Tutor Submit Answer Practice Another Version -/3 POINTS LARCALC11 8.6.505.XP.MI. MY NOTES | ASK YOUR TEACHER Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n=4. Compare these results with the approximation of the integral using a graphing utility. (Round your answers to three decimal places.) tan x x Trapezoidal Simpson's graphing utility Need Help? Read Watch It Mattorit Talk to a Tutor

Answer 1

4 we have hawn 1/2 Sin (al, da n=4 n an= b-a = 5 - 0 = 4 5 1 2 Divide the interval [o, Jr. III] into n=4 subintervals of length anda Jit a=0, JA JE, SAJT, Seva Tas Ja JT f(no) = f(a) = f(0) = 0 Hi) = f ( JE JT ) = sin(10 )) - sa centras) fCN2) = f (JEST ) = sin ( ()") = sin( terus #) = f ( V ST) - since Ja 57) = sinpomu) flmu) - FL VOJT ) = sin( (34T*)"= sin() By Tropezoidal rule, S fon) dx = An (fcmoot@fCm+3fCm2) +---+af(xnx) + f(mn)] Jos sinen") din = ax [fcha) + d-f(41)+ 0#(me) + 0FCM3) HfC143] va s 10+ a sinehou) + a sve to not asing such ) + sing ]

16 S7/2 - JBJT ( a sin Chew)+ a singelingt asing put) + sine tus] = 0.369461 I sin(uschen 0.3695 By Trapezoidal rule s sin(x) du = 8:3695 ВЫ Simpsons таи s flu) dn = 4 [ f(mo)+ 4400) + 2 f(x2)+... fluns] * S Singw'dm = AM [Amo) + 44(41) + 84(42 )+44(49) + f(Mus] = Jout Coty sin tids) + asing and +4 5. ( pour ? ) + since 2] 2 Lley 64 3189 I 1024 0.395330 sin (n) dn 013953 Jile .. By simpson's rule s sin (m) dn = 0.3953 By graphing utility St12 & sincm", dn = 0.29185 ř 0.2919 Trapezoidal simpson's 013695 0.3953 0.2919. graphing utility