6.5 Notes.pdf - YOLL MAM NW 2‘0 V3 “\3(M31333...

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Unformatted text preview: YOLL, MAM; NW 2‘0 V3 “\3 (M31333 0: (A (Rwy-94g :3, 3 3:: m3 3-3 3 \N 3‘ + 6.5 — Avera e Value of a Function (A 33 H» A L \NOW U (do? 23;" Row ‘ro X «N33 ‘53 ‘13: ”U . ' Average Value of f‘x) U\ h («JV ‘0“ “‘3 2" A “13‘ng 433M143, AME-2 (h (Shirt-w ‘flmfiw Lnuox \ug MAL. Luna/0“ 6“ 033133333, MNL 1 b \I 307$ e erage value of f(x) on The ih’rerval [a b] is define ’ro befav = fljflxwx $292203 2' \‘N 330303,. “M 4233-33“, INN (”an ”2""‘2‘L 63 k 030333. 7"”: ( ¥ ‘1 \ \AL \WW 1.9,." 7 \_ V3,, wwm {\32\d (X ' ‘:E\_ U‘ 00‘ 2 3—3—3“ ’ Xur‘ ; \NW‘x 35mph \\\<L 03“» ‘ 0“ \3 $4" /\\0\3 cum 3‘33,» L “3““ W3 we, mm @0me “3k (NULr‘MJ‘L \HKML Y‘R’O (XX : RN33 \3n3\Lf “‘3" i \1‘ (KS; 3 “K \5 ‘r \\&\\“"‘M {Gum W \F’ 332M333} 363333 3.33 J 33/ 'RLIB §)§§K\A\X:Wrx\ \N“\\Ur\ \5 OJV‘ £35333“- (\L 3, 0% W (M 3 333332 , he MeVngJ? Thearem 3o ‘33 3“ 333 33,33 3332533 If f is CQElflle ous on [a, b], Then there exis’rs a number (3 in [a, b] such Tha’r: m, b @b—l‘ajf‘x’dx ~Tht33 \s dL‘vM\\»‘ 3 333393 , \NNW‘Q ~32 “\3 33.3.3 3 r3 33 33 u 9 D ‘\ . b _ ”M 3 ’ (“Mk That Is, If(X)dX ‘flb -0)é3333333\ \J 02 \WL 3 Q 5 ‘3' \nQN-fi ‘\' a 2 - ‘ * 936333033“ 533$“ e Tkmk 0‘: 0333333 3‘3 3 ‘33? / mo“ WW U (\ \ \Ke.\ o\"\ *0 \ (X \(k 0(F\\ “EN 1”“ ‘ ' ”‘3‘ 2”? '13 (My . 3- 2‘, 33'3" (5 3 3 3.3 3. «3‘2 L \3}: ‘2‘" . 5 \ I \W 6‘ (\ L ‘x 0%, W (m L LJ\ (akl'v\€!)\ i» ' 3 <3 b , \, bowl \3 (Ho ¥-"\\I Q‘NMS ERAAX (fig/3736:? 9‘92““ WW“ “$30 3 Arm (3‘3 33 33033533 ERMA. mo‘mh (‘xhkk \XMMI‘ quvw (3(3pr \TEVW ‘5 3' 0 m, L 3333- 35 3133 cm 33 3 3L». 33 W33 ‘ A3333} With/UAJK { ‘K‘ASLRKQJ 0% C URAV \f\ U\ V (9Page15 “:3 ( \ Q,<3\J\0\\5 \I 0\\U\3V EQJWJMM Wm 333304 Examgle #1 Find The average value of The funcTion on The given inTerval. f(x)= 3x2+ 8x, [ 1 WW TX m *1 M MERIT :AVQCSKCWT KIM Examgle #2 Find The average value of The funcTion on The given inTerval. g=(x) 3 cosx, [,rr—/2 1%2] C 03 \AL \ S an (L \1 LA LIA I“ OL“ WI <T\ 1 . r O) 1%. ‘% Effigy; (MI : WV? 8 9095i (THC ~T§ WT L , 1T ? 1X / 'm SCIISTL<\V\: Tfiéb‘nfl: W, 11 § Q :qu - IjzagITII QUQ‘\' V‘\ J\ 0¢3 ‘QUV‘ A‘Wurfi Sq M UAW ‘mok (j Y Example #3 \J/ Zfléflivxziixfx‘fi””Na/rm ok a x M * M b. Find c such ’rthf(c) = fov V“ 2.9 c. Ske’rch f & 0 red ngle whose dred equals The area u der f. ( V Rug» 9 . s\ (:1 ' H \hlky‘xfl‘ikia)“ WW «SON :3} Q §)\K’L“‘1x’r W5 >L NWK ‘ :\ VHF. 5:i'§fi‘ 0x X ”L A c, b \ b Suht/l Q ~19 +\ : 1 Q Fm): 9271\W:\ L ‘ v 2. c, M 0 sex: and“: CF (Mg L u m 2:" 0 “A? sMg-Mh WWW L: 0 Lu. L “W 5“ \s \N o\ \ m ¥ \\\, x» W W C‘%%k<fifi3\& (X ” F Ox W W EV \OLK WQ/Xi \ R) ‘1‘ 5 QWW‘ :wdnm :36 Mm work VP Examgle #4 \\ / Forf(x)=1/xon[1,3] (\(Pr My“ \ 0. Find fav b. Find c such ’rhd’r f(c) = fov { Ske’rch f & 0 red ngle whose dred equals The drejd under f. 2:. 2.. I \ x 3 \n’b) 1\ GO ¥d\\i‘“—r§(—\ 8‘ ’1; 0M4 JLZDH‘XU\ ”(j 1 \ : LG} I 1 CANE) IE Mdrino ...
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