Question

Please show all work and answer

5) For each of the integrals in problems a c below, first sketch the corresponding area, and then approximate the area using the right and left endpoint approximations and the Trapezoid Rule, all with n = 4 . From your sketch alone determine if each approximation is an overestimate, an underestimate, or if there is not enough information to tell. Finally determine the value of n for which the Simpson Rule would approximate the area within 0.000001. Please use the bottom and back this page to do your work. c) cos(tan x)dx 1.sec хах a) J Inxdx b) -1

Answer 1

uxs a Rna - 0.6314,.0 38612 u An 1.38 6294, sns) 1.603438 aco uning right ena boinz ha 1 2 3 4 S 74 gi 4.78 1/0493 147 +1.038612 +1.386294 +1.60 g 438] = 478749nd num us awerestima .1780530 underestima [04 О. 693147 +1.098612 +1.3842g] +2(0.6 33147 +10 9k 12+13823+3 3.982712undr estimaa the anca usithin b.oosos 18o n4 1024-6 186 (o.osoool) 1V 34,133 n

b. 4 .1139u91 1.130 9+1)2.564302 |2.5643c 2. Over estimate = = o.sfl. 850816 +(.1394 gy +1+1. I39494} = 2.564802 2.564902) I overe End- 1.350816 +2 (1.133494 1 +.1384) 1.8soBid -| 2. S 6 4362 |sver estimate

Lo)Co.as) 0.3676 = 0.2S [0. g 676 + 08s 4 st 0.5366+00,347 = 10.608025| |andar estimate Ci Usiig latt ena bank o.as .3676+0 354+0.53 loyeresti mala | (с. 854 675 Ci) rabe zstaal vula : 4oso.stf (0-7 = o.ns [53508] =[0.7313S] /undaretimta