Spring 2017 Final Review

Transcription

1 Calculus s [w0o1w7^ nkiuhtqa] HScoQfZtEwFa`rgeo lltlycm.z t mailllz Rr`ihgUhmtCsc TrgehsfeurMvoehdG. Spring 017 Final Review Solve each related rate problem. Name 1) Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of cm/min. How fast is the area of the pool increasing when the radius is 10 cm? Date Period For each problem, approimate the area under the curve over the given interval using right endpoint rectangles. You ma use the provided graph to sketch the curve and rectangles. ) = + ; [-3, 1] T ]K0F1Q7U QKQuhtEaZ OSMo\fatiw]aBrHec cldlgcg.o z qallls rfibgih_tss_ Qrfeuswe`rkvYeodz.k \ MSawdneC vwmintihh IIznaf]iZnOibtgeO KCtadlNcQuQl\uEsT. -1-

2 For each problem, find the area under the curve over the given interval. Set up, but do not evaluate the integral. You ma use the provided graph to sketch the curve and shade the region under the curve. 3) = ; [, 5] Evaluate each sum. ) Sk = 1 (1k + ) Evaluate each indefinite integral. 5) 30 5 d) d 7) -1 d) 3cos d 9) - d10) e d A YL0o1C7A CK[uvt_aa HSQoNfetMwMaFrbeo OLVLkCc.[ Y LAJlolS oroiggehptdsn rrcersbeuryvaendk.p W ]MJaKdYeu hwtigtrhr pirnmfti^nzirtee iczanlpcluflvuhsc. --

3 11) Write an integral to find the area pictured ) Describe what negative area represents in Calculus. Does the meaning change if ou integrate to find area with respect to instead of with respect to? Evaluate each definite integral. 13) ( ) d 1) -p - p -cos d Evaluate each indefinite integral. 15) sec tan3 d1) (3 + 1) d \ o^0k1f7r HKQu]thaG oscojfjtywsaarex PL^LGCg.K g [AAlJlR ]raisgvhrt\sn QrTeFsSesrMvZeQdp. n rmgadet nwaistzhc SIhnOfUiNnFi\tOeT tcfaklocdubl^uhsd. -3-

4 Evaluate each indefinite integral using integration b parts. u and dv are provided. 17) ln d; u = ln, dv = 1 d 1) cos d; u =, dv = cos d Evaluate each indefinite integral. 19) 3( 9 + 5) d A particle moves along a coordinate line. Its velocit function is v(t) for t ³ 0. For each problem, find the displacement of the particle and the distance traveled b the particle over the given interval. 0) v(t) = -3t + 5t - 19; 3 t T fl0v1p7i CKquotGa^ gsaojfathwqaxrxe wlnlucv.h V haslhlf ar`ipghhwtlsu BrOess_e^rGvLeQdQ.j S RMgahdReQ QwiJtuh] SIonmfHifnsiOtNeX lcvawl^cauglouqsw. --

5 For each problem, find the area of the region enclosed b the curves. You ma use the provided graph to sketch the curves and shade the enclosed region. 1) = , = =, = , ) = + + 3, = + 3, = -5, = For each problem, find the volume of the solid that results when the region enclosed b the curves is revolved about the -ais. 3) = - + 1, = 0, = 0, = 1 s in0p1s7c rkzuytoai ksgo\fmtgwiaarsee clwlzcg.s o JAClGlv MrZiqgvh_tzsi zreuscedrkv\eid\.z n HMRagdOeW iwqiqtthq UIznAfTiBnniKtLeT ]CtarlFcJuclpuhsm. -5-

6 For each problem, find the volume of the solid that results when the region enclosed b the curves is revolved about the -ais. ) = + 1, = 1, = 1 For the following questions name the method ou would us to integrate each problem. Select (A) for u-substitution Select (B) for integration b parts Select (C) for Re-write. 5) 3 ( + 5) 5 d ) ln d 7) cos sin d) 3 csc d g A[01V7b YKVuethaB CSSovfrtkwKagrFed QLeLQC.W ^ `Aql\lW _rkiogqhatds SrwedsPeUrvTe[dz.E T ummazdbe DwEiYtFhb miqnmfxicniittaew gc]aqlpceujl\urs. --

7 Calculus q Vu0O1k7o HKCuXtRa OSZo^fVtnwLardeQ RLXLbCl.j U DA]lnlz nrvirgghpt\sk Dr^escewrDvfegdQ. Spring 017 Final Review Solve each related rate problem. Name 1) Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of cm/min. How fast is the area of the pool increasing when the radius is 10 cm? 0p cm²/min Date Period For each problem, approimate the area under the curve over the given interval using right endpoint rectangles. You ma use the provided graph to sketch the curve and rectangles. ) = + ; [-3, 1] F ag0l1w7m RKmu\tFaE ISmoufTtww\aVrieM \LsLPCa.n HAlBlB DrbiVgYhftEsh PrzezsVeKrRvMeJdi.G m rm]a]dej zwdiotmhg pizn^frihnzintoej VCpalAc[ugl]uYss. -1-

8 For each problem, find the area under the curve over the given interval. Set up, but do not evaluate the integral. You ma use the provided graph to sketch the curve and shade the region under the curve. 3) = ; [, 5] ) d Evaluate each sum ( ) Sk = 1 (1k + ) 17 Evaluate each indefinite integral. 5) 30 5 d 5 + C ) d C 7) -1 d ) 3cos d ln + C 3sin + C 9) - d 10) e d - ln + C e + C [ O_0q1^7Z RKFuktXaI QSuopfetYwVazreb FLwLpCs.I _ uavlrl TriiXgEhqtDsM ir\eqssezrsvre`dp.v T qmdaldweg owbiatnhs diunsfti]ngijtfey DCea]lFckuBlFu\sV. --

9 11) Write an integral to find the area pictured f () d 1) Describe what negative area represents in Calculus. Does the meaning change if ou integrate to find area with respect to instead of with respect to? Majorit of area is below the ais if ou integrate with respect to, and on the left of the -ais if ou integrate with respec to. Evaluate each definite integral. 13) ( ) d 3» 0.7 1) -p 1 - p -cos d Evaluate each indefinite integral. 15) sec tan3 d 1) (3 + 1) d 1 tan + C 7 (3 + 1) + C 7 F Ui0C1\7u LKguWtgas PSdoEfjtrwhaTrXeo VLQL]Cb.u e faulwle ^rciqgrhcteso trcetsgegrwvende.m K TMNasdkeR WwHiatThc JIKntfPiYnXiNtMeb ACmaYlscXuol]uXsO. -3-

10 Evaluate each indefinite integral using integration b parts. u and dv are provided. 17) ln d; u = ln, dv = 1 d 1 1 ln - + C 1) d; u =, dv = cos d cos sin + cos + C Evaluate each indefinite integral. 19) 3( 9 + 5) C d A particle moves along a coordinate line. Its velocit function is v(t) for t ³ 0. For each problem, find the displacement of the particle and the distance traveled b the particle over the given interval. 0) v(t) = -3t + 5t - 19; 3 t Displacement: Distance traveled: 153 7» 5.93 u id0w1n7d CKfuwtVaP RSSoRfCtcwpaVr`eB rltl^cq.s `AVlllX ]riiogehtsh mr\ehsrekrsvue[do.a B ZMOaIdveZ twdi]tqhu IvnifGidn_ittgei WCtaYlHc]uPlsuks_. --

11 For each problem, find the area of the region enclosed b the curves. You ma use the provided graph to sketch the curves and shade the enclosed region. 1) = , = =, = , ) = + + 3, = + 3, = -5, = ( = ( )) d ( ( + 3)) d + 0 ( ( + + 3)) d = 13 - For each problem, find the volume of the solid that results when the region enclosed b the curves is revolved about the -ais. 3) = - + 1, = 0, = 0, = 1 p 0 1 ( - + 1) d = 15 p» 1.7 ] \T0I1A7N VKvuutlad QStopfqtAwzatrMel ULTLrCg.U w YAslIlV `rbitg]hbtxs\ lroeesve^rbviehdm.u u EMdaDdNev Awui\tQhB GIGnEfkiunHiDtYem C[aOlnckuzlmuzss. -5-

12 For each problem, find the volume of the solid that results when the region enclosed b the curves is revolved about the -ais. ) = + 1, = 1, = 1 p 0 1 (( + 1) - 1) d = p».73 For the following questions name the method ou would us to integrate each problem. Select (A) for u-substitution Select (B) for integration b parts Select (C) for Re-write. 5) A 3 ( + 5) d 5 ) ln d B 7) cos sin d ) 3 csc d C A L eg0h1f7b WKcuDteaT psuohfxtvwnaarxed plqlscs.m G sa^ljld lreivgihet_sy frnejstehryvwehdf.t n ^MZaWdXeC twditthhu NIQnZfkiInCiCtzeJ JCWaQlUcKuEl^u[sV. --