LARSON CALCULUS Ch05 Integration and Applications

1. Find ithe iindefinite iintegral i iand icheck iyour iresult iby idifferentiation. A) B) C) 12 D) E) Ans: A 2. Evaluate ithe iintegral i . A) B) C) D) E) Ans: D 3. Find ithe iindefinite iintegral i iand icheck iyour iresult iby idifferentiation. A) B) C) D) E) Ans: D 4. Use ialgebra ito irewrite ithe iintegrand; ithen iintegrate iand isimplify. A) B) C) D) E) Ans: B 5. Find ithe iindefinite iintegral iand icheck ithe iresult iby idifferentiation. A) B) C) D) E) none iof ithe iabove Ans: A 6. Evaluate ithe iintegral i . A) B) C) D) E) Ans: D 7. Find ithe iindefinite iintegral iand icheck ithe iresult iby idifferentiation. A) B) C) D) E) Ans: D 8. Evaluate ithe iintegral i . A) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i B) C) D) E) Ans: C 9. Evaluate ithe iintegral i . A) B) C) D) E) Ans: A 10. Evaluate ithe iintegral i . A) B) C) D) E) Ans: E 11. The igraph iof ithe iderivative iof ia ifunction iis igiven ibelow. iSketch ithe igraphs iof itwo ifunctions ithat ihave ithe igiven iderivative. A) B) C) D) E) Ans: B 12. Find ithe iparticular isolution ithat isatisfies ithe idifferential iequation i iand iinitial icondition i . A) B) C) D) E) Ans: C 13. Find ia ifunction ithat isatisfies ithe iconditions i . A) B) C) D) E) Ans: B 14. Find ithe icost ifunction ifor ithe imarginal icost i iand ifixed icost iof i i(for ix i= i0). A) B) C) D) E) Ans: C 15. A iball iis ithrown ivertically iupwards ifrom ia iheight iof i10 ift iwith ian iinitial ivelocity iof i40 ift iper isecond. How ihigh iwill ithe iball igo? A) 85.0000 i ift B) 28.7500 i ift C) 35.0000 i ift D) 65.0000 i ift E) 88.6000 i ift Ans: C 16. An ievergreen inursery isells ia icertain ishrub iafter i8 iyears. iThe igrowth irate iof ithe ishrub iis igiven iby i , iwhere it iis ithe itime iin iyears iand ih iis ithe iheight iin icentimeters. iThe iseedlings iare i14 icentimeters itall iwhen iplanted i(t i= i0). iHow itall iare ithe ishrubs iwhen ithey iare isold? A) 166 icentimeters B) 172 icentimeters C) 208 icentimeters D) 222 icentimeters E) 270 icentimeters Ans: D 17. Identify and i ifor ithe iintegral i . A) iand i B) iand i C) iand i D) iand i E) iand i Ans: B 18. Identify iu iand i ifor ithe iintegral i . A) iand i B) iand i C) iand i D) iand i E) iand i Ans: C 19. Find ithe iindefinite iintegral iof ithe ifollowing ifunction iand icheck ithe iresult iby idifferentiation. A) B) C) D) E) none iof ithe iabove Ans: D 20. Evaluate ithe iintegral i A) B) C) D) E) Ans: D 21. Find ithe iindefinite iintegral iof ithe ifollowing ifunction iand icheck ithe iresult iby idifferentiation. A) B) C) D) E) none iof ithe iabove Ans: D 22. Evaluate ithe iintegral i A) B) C) D) E) Ans: E 23. Find ithe iindefinite iintegral iof ithe ifollowing ifunction iand icheck ithe iresult iby idifferentiation. A) B) C) D) E) none iof ithe iabove Ans: B 24. Evaluate ithe iintegral i A) B) C) D) E) Ans: D 25. Find ithe iindefinite iintegral iof ithe ifollowing ifunction iand icheck ithe iresult iby idifferentiation. A) B) C) D) E) i i i i i Ans: B 26. Find ithe iindefinite iintegral iof ithe ifollowing ifunction iand icheck ithe iresult iby idifferentiation. A) B) C) D) E) Ans: A 27. Use iformal isubstitution ito ifind ithe iindefinite iintegral i . A) B) C) D) E) Ans: D 28. Find ithe iequation iof ithe ifunction if iwhose igraph ipasses ithrough ithe ipoint i iand iwhose iderivative iis i . A) B) C) D) E) Ans: B 29. The imarginal icost iof ia iproduct iis imodeled iby i , iwhen ix i= i3, iC i= i90. iFind ithe icost ifunction. A) B) C) D) E) Ans: C 30. Find ithe isupply ifunction i ithat isatisfies i iand ithe iinitial icondition ix i= i600 iwhen i . A) B) C) D) E) Ans: A 31. Evaluate ithe iintegral i A) B) C) D) E) Ans: A 32. Evaluate ithe iintegral i A) B) C) D) E) Ans: C 33. Find ithe iindefinite iintegral. A) B) C) D) E) Ans: D 34. Evaluate ithe iintegral i A) B) C) D) E) Ans: C 35. Use ithe iLog iRule ito ifind ithe iindefinite iintegral ifor i . A) B) C) D) E) Ans: C 36. Find ithe iindefinite iintegral. A) B) C) D) E) Ans: C 37. Find ithe iindefinite iintegral. A) B) C) D) E) Ans: D 38. Find ithe iindefinite iintegral. A) B) C) D) integral idoes inot iexist E) none iof ithe iabove Ans: A 39. Find ithe iindefinite iintegral. A) B) C) D) E) Ans: A 40. Find ithe iindefinite iintegral. i A) B) C) D) E) none iof ithe iabove Ans: D 41. Use iany ibasic iintegration iformula ior iformulas ito ifind ithe iindefinite iintegral i . A) B) C) D) E) Ans: E 42. Find ithe iequation iof ithe ifunction iwhose iderivative iis i iand iwhose igraph ipasses ithrough ithe ipoint i . A) B) C) D) E) Ans: C 43. Sketch ithe iregion iwhose iarea iis igiven iby ithe idefinite iintegral iand ithen iuse ia igeometric iformula ito ievaluate ithe iintegral. A) –318 B) 636 C) 336 D) 168 E) 12 Ans: D 44. Sketch ithe iregion iwhose iarea iis igiven iby ithe idefinite iintegral iand ithen iuse ia igeometric iformula ito ievaluate ithe iintegral. A) B) C) D) E) none iof ithe iabove Ans: D 45. Use ithe ivalues and to ievaluate ithe idefinite iintegral . A) 21 B) –9 C) 1 D) 11 E) –7 Ans: B 46. Determine ithe iarea iof ithe igiven iregion. A) B) C) D) E) None iof ithe iabove Ans: B 47. Evaluate ithe idefinite iintegral iof ithe ialgebraic ifunction. Use ia igraphing iutility ito iverify iyour iresults. A) –6 B) –6 C) 13 D) 18 E) –3 Ans: E 48. Evaluate ithe idefinite iintegral i . A) B) C) D) E) Ans: E 49. Evaluate ithe idefinite iintegral iof ithe ialgebraic ifunction. Use ia igraphing iutility ito iverify iyour iresults. A) –67.0832 B) –115.0555 C) 101.7168 D) 17.3168 E) –182.1386 Ans: A 50. Evaluate ithe ifollowing idefinite iintegral. Use ia igraphing iutility ito icheck iyour ianswer. A) B) C) D) E) Ans: B 51. Find ithe iarea ibetween ithe icurve i iand ithe ix-axis ifrom i . A) B) C) D) E) Ans: A 52. Find ithe iaverage ivalue iof ithe ifunction iover ithe igiven iinterval. on i[-3,3] A) 15 B) 52.5 C) 90 D) 10 E) 50 Ans: A 53. Find ithe iaverage ivalue iof ithe ifunction iover ithe igiven iinterval. on i[0,1] A) B) C) D) E) Ans: C 54. The irate iof idepreciation iof ia ibuilding iis igiven iby i dollars iper iyear, Use ithe idefinite iintegral ito ifind ithe itotal idepreciation iover ithe ifirst i iyears. A) B) C) D) E) Ans: A 55. Determine ithe igraph iwhose iarea i(the ishaded iregion) iis irepresented iby ithe iintegral. A) B) C) D) E) Ans: C 56. Find ithe iarea iof ithe ishaded iregion. A) B) C) D) E) Ans: B 57. Set iup ithe idefinite iintegral ithat igives ithe iarea iof ithe iregion ibounded iby ithe igraphs. A) B) C) D) E) Ans: D 58. The iintegrand iof ithe ifollowing idefinite iintegral iis ia idifference iof itwo ifunctions. Sketch ithe igraph iof ithe itwo ifunctions iand ishade ithe iregion iwhose iarea iis irepresented iby ithe iintegral. A) B) C) D) E) Ans: B 59. Find ithe iarea iof ithe iregion ibounded iby ithe igraphs iof ithe ialgebraic ifunctions. A) B) C) D) E) Ans: D 60. Find ithe iarea iof ithe iregion ibounded iby ithe igraphs iof ithe ialgebraic ifunctions. A) B) C) D) E) Ans: A 61. Find ithe iconsumer iand iproducer isurpluses iby iusing ithe idemand iand isupply ifunctions, iwhere ip iis ithe iprice i(in idollars) iand ix iis ithe inumber iof iunits i(in imillions). Demand iFunction i i i i i i i i i i i iSupply iFunction i i i i i i i i i i i i i i i i i A) a. i$2587.50 b. i$3725.00 B) a. i$5587.50 b. i$4725.00 C) a. i$2587.50 b. i$1725.00 D) a. i$1587.50 b. i$4725.00 E) a. i$3587.50 b. i$4725.00 Ans: C 62. The idemand ifunction ifor ia iproduct iis i , iwhere ip iis ithe inumber iof idollars iand ix iis ithe inumber iof iunits. iIf ithe iequilibrium iprice iis i , iwhat iis ithe iconsumer’s isurplus? A) $ B) $ C) $ D) $ E) $ Ans: B 63. Two imodels, i iand i , iare igiven ifor irevenue i(in ibillions iof idollars iper iyear) ifor ia ilarge icorporation. iBoth imodels iare iestimates iof irevenues ifor i2007 ithrough i2011, iwith it i= i7 icorresponding ito i2007. iWhich imodel iis iprojecting ithe igreater irevenue? iHow imuch imore itotal irevenue idoes ithat imodel iproject iover ithe ifive-year iperiod? A) The imodel i iprojects igreater irevenue ithan i . billion B) The imodel i iprojects igreater irevenue ithan i . billion C) The imodel i iprojects igreater irevenue ithan i . billion D) The imodel i iprojects igreater irevenue ithan i . billion E) The imodel i iprojects igreater irevenue ithan i . billion Ans: C 64. The irevenue ifrom ia imanufacturing iprocess i(in imillions iof idollars iper iyear) iis iprojected ito ifollow ithe imodel i ifor i10 iyears. iOver ithe isame iperiod iof itime, ithe icost i(in imillions iof idollars iper iyear) iis iprojected ito ifollow ithe imodel i , iwhere it iis ithe itime i(in iyears). iApproximate ithe iprofit iover ithe i10-year iperiod, ibeginning iwith it i= i0. iRound iyour ianswer ito itwo idecimal iplaces. A) imillion B) imillion C) imillion D) imillion E) imillion Ans: A 65. Use ithe iMidpoint iRule iwith in i= i4 ito iapproximate ithe iarea iof ithe ifollowing iregion. A) 3 B) 8 C) 2 D) 1 E) 6 Ans: C 66. Use ithe irectangles ito iapproximate ithe iarea iof ithe iregion. iCompare iyour iresult iwith ithe iexact iarea iobtained iwith ia idefinite iintegral. i A) a. iThe iapproximate iarea: i3 b. iThe iexact iarea: i2 B) a. iThe iapproximate iarea: i2 b. iThe iexact iarea: i3 C) a. iThe iapproximate iarea: i2 b. iThe iexact iarea: i1 D) a. iThe iapproximate iarea: i2 b. iThe iexact iarea: i2 E) a. iThe iapproximate iarea: i1 b. iThe iexact iarea: i2 Ans: D 67. Use ithe iMidpoint iRule iwith in i= i4 ito iapproximate ithe iarea iof ithe iregion ibounded iby ithe igraph iof i iand ithe ix-axis iover ithe iinterval i[ ]. A) 13.5671 B) 13.1273 C) 13.3364 D) 13.1250 E) 14.1250 Ans: D 68. Use ithe iMidpoint iRule iwith in i= i4 ito iapproximate ithe iarea iof ithe iregion ibounded iby ithe igraph iof i iand ithe ix-axis iover ithe iinterval i[0,1]. A) 3.7882 B) 3.3484 C) 3.5575 D) 4.3461 E) 3.3461 Ans: E 69. Use ithe iMidpoint iRule iwith i ito iapproximate ithe iarea iof ithe iregion ibounded iby ithe igraph iof iand ithe i-axis iover ithe iinterval. iSketch ithe iregion. A) The iapproximate iarea iis: i B) The iapproximate iarea iis: i C) The iapproximate iarea iis: i D) The iapproximate iarea iis: i E) The iapproximate iarea iis: i Ans: C 70. Use ithe iMidpoint iRule in i= i4 ito iapproximate ithe iarea iof ithe ifollowing iregion. A) 2.5 B) 1.2 C) 1.5 D) 1.9 E) 2.3 Ans: C 71. Estimate ithe isurface iarea iof ithe ipond ishown iin ithe ifigure iusing ithe iMidpoint iRule. A) B) C) D) E) Ans: B 72. Estimate ithe isurface iarea iof ithe ioil ispill ishown iin ithe ifigure iusing ithe iMidpoint iRule. A) 481.6 B) 301.6 C) 311.6 D) 431.6 E) 381.6 Ans: E 73. Use ithe iMidpoint iRule iwith i ito iapproximate i where i . iThen iuse ia igraphing iutility ito ievaluate ithe idefinite iintegral. iCompare iyour iresults. A) a. iMidpoint iRule: i i b. iGraphing iutility: i B) a. iMidpoint iRule: i i b. iGraphing iutility: i C) a. iMidpoint iRule: i i b. iGraphing iutility: i D) a. iMidpoint iRule: i i b. iGraphing iutility: i E) a. iMidpoint iRule: i i b. iGraphing iutility: i Ans: D 74. Estimate ithe isurface iarea iof ithe igolf igreen ishown iin ithe ifigure iusing ithe imidpoint irule. A) 780 B) 156 C) 1404 D) 1502 E) 524 Ans: A