UIC - MCS 181 - Class Notes - Week 5

View Full Material##### School: University of Illinois at Chicago

##### Department: Math

##### Course: Calculus II

##### Professor: Martina Bode

##### Term: Fall 2016

##### Tags: approximate intergration, trapezoid rule, and Simpson's Rule

##### Name: Class Notes 9/19

##### Description: 7.7 Approximate Integration -Trapezoid Rule -Simpson's Rule

##### Uploaded: 09/19/2016

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Unformatted text preview: ,L :72. \ ‘\ 7.7 Approximate Integration Question 1. Snow is falling over a three hour period at the following rates. Appran— z'mate the total amount of snow that fell during this period. time/hours 0 0.5 1 1.5 2 2.5 3 LCX) Rate/inches per hO’U/f‘ 1 0.5 1.5 1.5 1 0.5 0 ((1) Find the average of the left—endpoint and the right—endpoint sum for n = 6. (kva' 0w Ibex Lug: / 5 “ 9 / do» — K?" (,"J 0? 'A‘C‘. ;,on‘f:/ + V ‘I \.l _ r (24/ ) ' \ J / /M .\\V / 1: o.Y‘ (:1 o ‘h‘v'VCVP'Q’L/Okl C'L | Z (.2 «(CHM/13H s (Xx;va 'm c/i MC“. \ch f ‘ ">c‘\ v“, /./ téx) ‘v 0K\KJ\C5 ((+33. + \5 ms + \ \, \ / ‘ .5 NH Moog/10kg : J Y 0\E . yo /7Q()<) V c\.\\4x'6.5 _ //‘\. ?k?lé’ I x 71 gave); 7 {7942.3 )‘:\Z,,'l">\ \ ‘TU : 3:7, LIL” )f Rb> YT “Vex ZOKAOJ MHZ \ ‘ ch v‘xc/UL ‘ VW "‘6 g; -_; K) \v‘x-he/Y V"fN\ § ' dureer \i n e bo/hrvwxx f u ‘» 0-6 ° +0me CM’ “MIL O? Wax. F-Q’Ly\ d \20 n“* Evmw m ' t 3 ms at a MOS-6 HI “ML CHOW] LL' SEO $1 $2 $3 1134 "' III” “35) 90 2/1 312 3/3 3/4 yn Ax Tn = 7(90 +291 + 292 + 2293 + 2.714 + 2% + ' ' ' +29n—1 +yn) Ax ‘Q'm 47.0» ': A2: T’ ‘ n even: Sn = ~3—(yo + 4:111 + 2:92 + 4.713 + 2314 + 4% + - - - 4341.4 + yn) y l W Snow is falling over a three hour period at the following rates. Approximate the total amount of snow that fell during this period. time/hours 0 0.5 1 1.5 2 2.5 3 ‘5 J Rate/inchesperhOur 1 0.5 1.5 1.5 1 0.5 0 evx r-A wé Hm Pk (17) Use Simpson’s Method to approximate the snow. . V WW“ ‘ L“‘*g“"“ <H ELL-5:14 2. 4;”..5} + v: x.‘ J“ J r z i W * )0] U l’f ‘- . 1 4dr . , _ Questlon 2. Check that: 7r 2 . Then use Simpsons rule with n = 2 to . 0 1 + $2 —’...————“ .Q/\l m v/ approximate 7r. ‘ I ,i )4, O x J l M\ rr'??— [I = mehmhc ’1 qwc?mhl ‘H “go?i‘?y 2.143;; Ll MS 2‘ o + 7‘ _ . 'T‘ » - ‘ l - 5.: “A . up- + m) 1T : EJXHWQUH . \A I. .2 l/ ’— L11» ., v a . 7’” w I ’H‘I‘W’ (7)00 fl dsd ‘VV'Q :' r2: ( ’l‘ ‘12? ) '3 [UV ‘ (1:! J 01 1+ <7? x‘ (Ap\ngy-\’sr\'1C\+{ “AW S‘\y\q%§bn7’ 3" > 37 “v 30 [.3 (ll/50““g // Question 3. Use (a) Trapezoidal Rule, and ( b ) Simpson’s Rule to approsiimate the 5 integral —— do: with a subdivision into four subinteruals. 1 “5 >< \ 5 Mei 4:”) £120 '60 .‘2/0 15’ Ill \L‘z 1(1~U0+-2,5Q+ ZvZO—klah.+t\a\r2> 2 .1 + ,,,, ,, 3 “Ms ‘: - a??? qoikdxroxh'c [VACjonOx/m‘k?o {‘15an 'JW CAHQV‘mPV +0 Hind 0» Rwabmm AX UK..qu 1M) sin oux \ Cl CKJ. ‘~"-'UV\‘[5

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