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Unformatted text preview: _APCalculus _ . Name'KEj - ' Chapter 5 Review Evaluate Thé inTe hal withom' usin a calculator. Show all work neaTl : V 1. :J‘3—2’Z dx 2‘. I7+3x 2 dx 3. I(3csczx)dx 7. [sec x tan xdx 8 [2 cos xdx . 9.1_[x(x2—1)dx 1-— M 3 w w . .k 3+ :él(5m’IF-5m0> :— 7‘1)‘ "le l" 4 ‘lz I“... "’5‘ l. '3 3; M alx = «3/3 Y 3 = 3, 3w 0W » 3 2'7 ”1 ”— :ﬁlxb’olx 11%.;l ”3" 503339‘ '1 :LXS’L’: :V‘lg 5 ,.m1 -132 43 Si). ”w ”’37" ’ ”LB-3 ; M” ”I 511:“va J37 W _ XL v 37' l UZ—glq «Ll 2 2:-Ha~a _«ns .3 < seyour‘calculm‘or‘fofilgw1+ '::alue 5 l . -- ff'l’ '39 "0 ' ii I z: 517 A 63(13_(,,le2)€+1 dx mag/{WWW 14 [3 dx (3” rumba/'7 EC 7F ~94 (ll) 3 linln+Cl72><+l)?< 31°)OO‘XH) ﬁsWtan/ﬁ x o 1) 00v 0'1, ‘9 6‘ en r" \l" \L W 9~ 09:3? ,l l 9'1“ 15. USe The graph of fshown in The figure. The shaded region A has an area of 1.5, and‘ 6 If(x)dx = 3.5. Find Thefollowing. a) lfmdx b) 6jf(x)dx c) j)f(x)ldx : . “El : L5 5 d) j-2f(x)dx _ e) j()2+f(x)dx ' , : l‘0'5l :: ,1 5,5) :0 (60+ Sub-[ICQO‘V : 7 =1 l 3+ 5. 6 7: f) The 9e value of f on [0, 6] 90 area {5 “mam-hm " 3-0 59mm .-= ﬁes) 3; l T 16. Find The exacT area of The region bounded by y: (2x - 1), The xsaxis, x : land x: 3 SkeTch a graph and show an inTegral SeTup. lax-'DM - 31.20043): El lﬂmﬁi: VHF—1&3) 0-03 :2. -17 Use The Trapezoidal Rule, wiTh 4 subinTervals, To approximaTe [(11)2dx. Show your seTup. x l 5ke+cha9mph- , ., 3(ga5)(6 may(w+.-wv)+(4titi+.327).. +(32‘H~ 25) = . SOC} A 3 18. Use The given Table of measuremenTs To esTimaTe The number of square meTers of land in a loT where 'Xand yare measured in meTers, as shown in’Thef‘igure below. The land is bounded by a I sTream and Two sTraighT roads ThaT meeT aT a righT angle. Show your seTup. 'a) Use a righrendpoinT Riemann sum b) Use a lefT endpoinT Riemann sum = lol3lf8ll+70+lfiﬂo\$+Q‘iir‘73Tle9-l... , A3“)ﬁSTmTS’TTWH-‘QVWBWTm ’ +53 +Lia.»,aa+o)' .. +72+b8+5uwa+a® ooLol ‘ 625 19. Use The Ted ThaT Rx 3)dx— — —4—~To evalua e he definiTe inTegrals wiThouT Using The FundamenTal Theorem of Calculus 20. The graph of The velociTy v(T), in fT/Sec, of a car Traveling on a sT-raighT road, for 0 < t_ < 50,- is shown above A Table of values for v(T), GT 5 second inTervals of Time T, is shown To The righT of The graph (0) During whaT inTervals of Time is The acceleraTion of The car posiTive? Give a reason for your \M‘p gﬂ/ answer. (O) 35) V (D: QL‘E) c 3 510.9125 oi— Mngﬂrﬁ lines o VU: , (45950) M”) are pOSI'hue, ‘19“th (b) Find The average acceleraTion of The car, in fT/secz, over The inTerval O_ -< t < 50 / AV : V050)— We) 1a....o __ 33.. “12’ AT: SOs-43 "" 50 m0 "’ 50 3 ﬁg NU (c) Find one approximaTion for The acceleraTion of The car in fT/secz, aT T: 40 Show The @ compuTaTions you used To arrive aT your answer Q‘\:O fﬂw LLHMmL M11. W ‘ le charvllImL +41» 35 550 45-40 , ' 49 35 .910 ‘W(d) ApproximaTe J-v(t)dt wiT a Riemann sum, using The midpoinTs of five subinTervals of equal . 0 lengTh. Using correcT uniTs, explain The meaning of This inTegral *Ioonw 4: bL\${ values Fireball: 5%. Io(I 2» + 30+ 7o+8i+¢o§ (25309 VLLW 16\$ W a 0"9 1‘ «we f: Mauve exmssgés m +0464 aislemcL Tim/Ltd in Helium +520 ’bt;EOS£C For The nexT Two problems, find The average value of The funcTion over The inTervaI, wiThouT using a calculaTor. 21. f()c)=3L—:l on [1,2] . 22. f(x)=sinx on [0,7r] ”L x 2 1X1 ' I W \ W l x2 I ”3 1T? >4 ---§ SmX ’— _——-o\x ., 5 ‘ Trio o , 2/4; T, V: 1 h— L yéng “ qwgl‘ l+x'ol>< :9“? I]? :@ ’ Ti \ ° :11 > .3... “ 3 n 3 “f (”'CDSTT—l- £030) Ti TI" 23. Use The TuncTion fin The figure and The funcTion gdefined by g(x)— — Jf(t)dt for This problem. at» circa, W 50 R‘Dd’t’ X30 040 X3 l a) CompleTe The Table ‘ wb'bhu) KmOkYAS b) PloT The poinTs from The Table in parT (a). c) Where does 9 have iTs minimum? Explain X: or 8: {2 changes onm Mwm To pusfehm d) Which four consecuTive poinTs on gore collinear? Explain x: OJI a 3 charges In x and gave, . Mt townhca car/h hnch (it Conawi’t'l'ﬁ‘W) raT9 xp e) BeTween which Two consecuTive poinTs does 9 increase aT T e greaTesT lain am 35:9; in and 1% inlcmal . ‘KS’T‘WllTW W 1’) Where does 9 have poinTs of In lecTion, if any Explain 15b 9»? -ll changes Wm Mormamo) Ta mcrmma I g) CompleTe The Table Sketch the region corresponding to each definite integral. Then evaluate each integral using geometric area formulas. [You re sketching the regions yourself. You would nor be provided with a graph 1 30. ‘The graph of f(x) consists of line segments and quarter circles as shown in the graph. What is the l- A ZINII WWIIIIII/ ‘ . value of 3f(x)dx? la‘kcmowyﬂrz Hm I— w lol’) +~i gm {in} - ».L “(9‘) gami— ((3)0 +z< (J'X (”+54 (allm'ﬁ Will .... __L . ;IJ,7,.I:L+HI ill—"HT. :—-'II' +t+A~€zIT I 4/ ...
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