Larson Calculus Ch06 Techniques of Integration

1. Identify iu iand idv ifor ifinding ithe iintegral iusing iintegration iby iparts. A) B) C) D) E) Ans: A 2. Identify iu iand idv ifor ifinding ithe iintegral iusing iintegration iby iparts. dx A) dx; i dx B) C) D) E) Ans: B 3. Use iintegration iby iparts ito ievaluate i A) B) C) D) E) Ans: A 4. Find ithe iindefinite iintegral. A) B) C) D) E) Ans: E 5. Use iintegration iby iparts ito ievaluate . iNote ithat ievaluation imay irequire iintegration iby iparts imore ithan ionce. A) B) C) D) E) Ans: A 6. Use iintegration iby iparts ito ifind ithe iintegral ibelow. i A) B) C) D) E) Ans: D 7. Find ithe iindefinite iintegral. A) B) C) D) E) Ans: A 8. Use iintegration iby iparts ito ievaluate i . A) B) C) D) E) Ans: E 9. Find ithe iindefinite iintegral. A) B) C) D) E) Ans: B 10. Find ithe iindefinite iintegral. A) B) C) D) E) Ans: E 11. Find ithe iindefinite iintegral. A) B) C) D) E) Ans: C 12. Find ithe iindefinite iintegral. A) B) C) D) E) none iof ithe iabove Ans: B 13. Evaluate ithe idefinite iintegral i . iRound iyour ianswer ito ithree idecimal iplaces. A) 828.111 B) 207.823 C) 118.290 D) 207.811 E) 79.245 Ans: C 14. Find ithe idefinite iintegral. A) B) C) D) E) none iof ithe iabove Ans: B 15. Use iintegration iby iparts ito ifind ithe iintegral ibelow. A) B) C) D) E) Ans: D 16. A imodel ifor ithe iability iM iof ia ichild ito imemorize, imeasured ion ia iscale ifrom i0 ito i10, iis i iwhere it iis ithe ichild’s iage iin iyears. iFind ithe iaverage ivalue ipredicted iby ithe imodel ifor ia ichild’s iability ito imemorize ibetween ifirst iand isecond ibirthdays. iRound iyour ianswer ito ithree idecimal iplaces. A) 3.318 B) 2.218 C) 4.118 D) 1.318 E) 2.018 Ans: E 17. Present iValue iof ia iContinuous iStream iof iIncome. iAn ielectronics icompany igenerates ia icontinuous istream iof iincome iof i million idollars iper iyear, iwhere it iis ithe inumber iof iyears ithat ithe icompany ihas ibeen iin ioperation. iFind ithe ipresent ivalue iof ithis istream iof iincome iover ithe ifirst i9 iyears iat ia icontinuous iinterest irate iof i12%. iRound ianswer ito ione idecimal iplace. A) $143.7 imillion B) $81.6 imillion C) $182.7 imillion D) $343.2 imillion E) $85.8 imillion Ans: B 18. Use ia itable iof iintegrals ito ifind ithe iindefinite iintegral i . A) i B) C) i D) E) Ans: A 19. Use ia itable iof iintegrals iwith iforms iinvolving i ito ifind ithe iintegral. A) B) C) D) E) Ans: E 20. Find ithe iintegral ibelow iusing ian iintegral itable. A) B) C) D) E) Ans: E 21. Use ia itable iof iintegrals iwith iforms iinvolving i ia i+ ibu ito ifind i A) B) C) D) E) Ans: C 22. Use ia itable iof iintegrals ito ifind ithe iindefinite iintegral i . A) B) C) D) E) Ans: B 23. Use ia itable iof iintegrals iwith iforms iinvolving i ito ifind i A) B) C) D) E) Ans: A 24. Use ia itable iof iintegrals ito ifind ithe iindefinite iintegral i . A) B) C) D) E) Ans: C 25. Use ia itable iof iintegrals ito ifind ithe iindefinite iintegral i . A) B) C) D) E) Ans: A 26. Use ithe iTrapezoidal iRule iand iSimpson’s iRule ito iapproximate ithe ivalue iof ithe idefinite iintegral ifor ithe iindicated ivalue iof in. iCompare ithese iresults iwith ithe iexact ivalue iof ithe idefinite iintegral. iRound iyour ianswers ito ifour idecimal iplaces. i A) a. iExact: i b. iTrapezoidal iRule: i c. iSimpson’s iRule: i B) a. iExact: i b. iTrapezoidal iRule: i c. iSimpson’s iRule: i C) a. iExact: i b. iTrapezoidal iRule: i c. iSimpson’s iRule: i D) a. iExact: i b. iTrapezoidal iRule: i c. iSimpson’s iRule: i E) a. iExact: i b. iTrapezoidal iRule: i c. iSimpson’s iRule: i Ans: E 27. Approximate ithe ivalue iof ithe idefinite iintegral iusing i(a) ithe iTrapezoidal iRule iand i(b) iSimpson’s iRule ifor ithe iindicated ivalue iof in. iRound iyour ianswers ito ithree isignificant idigits. A) a. iTrapezoidal iRule: i b. iSimpson’s iRule: i B) a. iTrapezoidal iRule: i b. iSimpson’s iRule: i C) a. iTrapezoidal iRule: i b. iSimpson’s iRule: i D) a. iTrapezoidal iRule: i b. iSimpson’s iRule: i E) a. iTrapezoidal iRule: i b. iSimpson’s iRule: i Ans: B 28. The irate iof ichange iin ithe inumber iof isubscribers i ito ia inewly iintroduced imagazine iis imodeled iby i i iwhere i iis ithe itime iin iyears. iUse iSimpson’s iRule i with ito iestimate ithe itotal iincrease iin ithe inumber iof isubscribers iduring ithe ifirst i6 iyears. A) 1870 isubscribers B) 1780 isubscribers C) 1800 isubscribers D) 1878 isubscribers E) 1987 isubscribers Ans: D 29. A ibody iassimilates ia i12-hour icold itablet iat ia irate imodeled iby i iwhere i iis imeasured iin imilligrams iper ihour iand i iis ithe itime iin ihours. iUse iSimpson’s iRule iwith i ito iestimate ithe itotal iamount iof ithe idrug iabsorbed iinto ithe ibody iduring ithe i12 ihours. A) 58.915 img B) 68.915 img C) 38.915 img D) 48.915 img E) 78.915 img Ans: A 30. Evaluate ithe idefinite iintegral i . iRound iyour ianswer ito ithree idecimal iplaces. A) 20.210 B) 16.873 C) 32.580 D) 26.395 E) 4.504 Ans: E 31. Evaluate ithe idefinite iintegral i dx. iRound iyour ianswer ito ithree idecimal iplaces. A) 6.144 B) 7.207 C) 4.541 D) 5.644 E) 4.881 Ans: D 32. The iprobability iof irecall iin ian iexperiment iis imodeled iby i iwhere ix iis ithe ipercent iof irecall. iWhat iis ithe iprobability iof irecalling ibetween i60% iand i90%? iRound iyour ianswer ito ithree idecimal iplaces. A) 0.432 B) 0.270 C) 0.710 D) 0.219 E) 0.936 Ans: A 33. Use ithe itable iof iintegrals ito ifind ithe iaverage ivalue iof ithe igrowth ifunction i iover ithe iinterval i , iwhere iN ithe isize iof ia ipopulation iand it iis ithe itime iin idays. iRound iyour ianswer ito ithree idecimal iplaces. A) 248.346 B) 1057.983 C) 246.346 D) 680.477 E) 682.451 Ans: C 34. The irevenue i(in idollars iper iyear) ifor ia inew iproduct iis imodeled iby i iwhere it ithe itime iin iyears. iEstimate ithe itotal irevenue ifrom isales iof ithe iproduct iover iits ifirst i3 iyears ion ithe imarket. iRound iyour ianswer ito inearest idollar A) $6579 B) $3291 C) $10,821 D) $15,830 E) $1138 Ans: B 35. Approximate ithe idefinite iintegral i"by ihand," iusing ithe iTrapezoidal iRule iwith i itrapezoids. iRound ianswer ito ithree idecimal iplaces. i A) 11.425 B) 11.381 C) 5.691 D) 8.569 E) 15.175 Ans: D 36. Use ithe iTrapezoidal iRule ito iapproximate ithe ivalue iof ithe idefinite iintegral i . iRound iyour ianswer ito ithree idecimal iplaces. A) 6.7643 B) 2.7931 C) 2.7955 D) 4.6552 E) 4.6615 Ans: C 37. Decide iwhether ithe iintegral iis iproper ior iimproper. i i A) The iintegral iis iimproper. B) The iintegral iis iproper. Ans: B 38. Determine ithe iamount iof imoney irequired ito iset iup ia icharitable iendowment ithat ipays ithe iamount i each iyear iindefinitely ifor ithe iannual iinterest irate icompounded icontinuously. i A) $210,000 B) $200,000 C) $220,000 D) $240,000 E) $230,000 Ans: B 39. The icapitalized icost i iof ian iasset iis igiven iby i iwhere i iis ithe ioriginal iinvestment, i iis ithe itime iin iyears, i iis ithe iannual iinterest irate icompounded icontinuously, iand i iis ithe iannual icost iof imaintenance i(in idollars). iFind ithe icapitalized icost iof ian iasset i(a) ifor i5 iyears, i(b) ifor i10 iyears, iand i(c) iforever. A) a. iFor i $253,901.30 b. iFor i $807,922.43 c. iFor i $4,466,666.67 B) a. iFor i $453,901.30 b. iFor i $807,922.43 c. iFor i $1,466,666.67 C) a. iFor i $453,901.30 b. iFor i $2807,922.43 c. iFor i $4,466,666.67 D) a. iFor i $453,901.30 b. iFor i $807,922.43 c. iFor i $4,466,666.67 E) a. iFor i $453,901.30 b. iFor i $807,922.43 c. iFor i $466,666.67 Ans: D 40. Approximate ithe iintegral iusing iSimpson's iRule: i , in i= i6. iRound iyour ianswer ito ithree idecimal iplaces. A) 1.161 B) 1.284 C) 0.850 D) 0.652 E) 1.017 Ans: D 41. Use iSimpson's iRule ito iapproximate ithe irevenue ifor ithe imarginal irevenue ifunction i iwith in i= i4. iAssume ithat ithe inumber iof iunits isold, ix, iincreases ifrom i12 ito i16. iRound iyour ianswer ito ione idecimal iplace. A) $1602.40 B) $678.36 C) $1346.14 D) $1439.03 E) $1230.54 Ans: D 42. Use ithe ierror iformulas ito ifind in isuch ithat ithe ierror iin ithe iapproximation iof ithe idefinite iintegral i iis iless ithan i0.0001 iusing ithe iTrapezoidal iRule. A) 25 B) 26 C) 24 D) 22 E) 23 Ans: E 43. A ibody iassimilates ia i16-hour icold itablet iat ia irate imodeled iby i , i iwhere it iis imeasured iin imilligrams iper ihour iand it iis ithe itime iin ihours. iUse iSimpson’s iRule iwith in i= i16 ito iestimate ithe itotal iamount iof ithe idrug iabsorbed iinto ithe ibody iduring ithe i16 ihours. A) 58.88 B) 34.88 C) 54.33 D) 46.88 E) 64.90 Ans: C 44. Decide iwhether ithe ifollowing iintegral iis iimproper. A) no B) yes Ans: B 45. Evaluate ithe iimproper iintegral iif iit iconverges, ior istate ithat iit idiverges. A) B) C) D) E) diverges Ans: D 46. Evaluate ithe iimproper iintegral iif iit iconverges, ior istate ithat iit idiverges. A) B) C) D) E) diverges Ans: E 47. Determine iwhether ithe iimproper iintegral idiverges ior iconverges. iEvaluate ithe iintegral iif iit iconverges. A) converges ito i0 B) converges ito i3 C) converges ito i D) diverges ito i E) diverges ito i Ans: C 48. Suppose ithe imean iheight iof iAmerican iwomen ibetween ithe iages iof i30 iand i39 iis i68.5 iinches, iand ithe istandard ideviation iis i2.7 iinches. iUse ia isymbolic iintegration iutility ito iapproximate ithe iprobability ithat ia i30-to i39-year-old iwoman ichosen iat irandom iis ibetween i5 iand i6 ifeet itall. A) 0.1772 B) 0.9017 C) 0.5707 D) 0.8547 E) 0.4257 Ans: B 49. A ibusiness iis iexpected ito iyield ia icontinuous iflow iof iprofit iat ithe irate iof i$1,000,000 iper iyear. iIf imoney iwill iearn iinterest iat ithe inominal irate iof i8% iper iyear icompounded icontinuously, iwhat iis ithe ipresent ivalue iof ithe ibusiness iforever? A) $12,600,000 B) $12,510,000 C) $12,500,000 D) $1,250,000 E) $1,350,000 Ans: C 50. Find ithe icapitalized icost iC iof ian iasset iforever. iThe icapitalized icost iis igiven iby i iwhere i iis ithe ioriginal iinvestment, it iis ithe itime iin iyears, ir i= i12% iis ithe iannual iinterest irate icompounded icontinuously, in iis ithe itotal itime iin iyears iover iwhich ithe iasset iis icapitalized, iand i iis ithe iannual icost iof imaintenance i(measured iin idollars). iRound iyour ianswer ito itwo idecimal iplaces. A) $1,525,000.00 B) $1,275,000.00 C) $1,108,333.33 D) $1,299,218.75 E) $1,247,222.22 Ans: E