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All Textbook Solutions for Calculus and Its Applications (11th Edition)

63. Accumulated sales. Raggs, Ltd., estimate that is sales are growing continuously at a rate given by , Where is in dollars per day, on day t. a. Find the accumulated sales for the first 5 days. b. Find the from the 2nd day through the 5th dat. (This is the integral from 1 to 5.) 64. Accumulated sales. Melanie’s Crafts estimates that its sales are growing continuously at a rate given by , where is in dollars per day, on day t. Find the accumulated sales for the first 5 days. b. Find the sales from the 2nd day through the 5th dat. (This is the integral from 1 to 5.) 65E Credit Market debt. The annual rate of change in the national credit market debt (in billions of dollars per year) can be modeled by the function D(t)=33.428t+71.143, Where t is the number of years since 2009. (Source: Federal Reserve System.) Use the preceding information for Exercises 65 and 66. By how much did the credit market debt increase between 2011 and 2015?67E Industrial Learning Curve A company is producing a new product, and the time required to produce each unit decreases as workers gain experience. It is determined that T(x)=2+0.3(1x), Where T(x) is the time, in hours, required to produce the xth unit. Use this information for Exercises 67 and 68. Find the total required for a worker to produce units 1 through 20; units 20 through 40.The rate of memorizing information initially increases. Eventually, however, a maximum rate is reached, after which it begins to decreases. Suppose an experiment finds that rate the rate of memorizing is given by M(t)=0.009t2+0.2t, Where M(t) is the memory rate, in words per minute. How many words are memorized in the first 10 min (fromt=0tot=10)?70E 71E The rate of memorizing information initially increases. Eventually, however, a maximum rate is reached, after which it begins to decreases. See Exercises 70. How many are memorized during minutes 10-17?Find 73. 74E 75E 76E 77E Find s(t) a(t)=6t+7,withv(0)=10ands(0)=20 79E 80E Distance and speed. A motorcycle accelerates at a constant rate from 0 mph (v(0)=0) to 60mph in 15 sec. how far has it traveled after 15 sec? (Hint; Convert seconds to hours.)82. Distance and speed. A car accelerates at a constant rate from 0mph to 60mph in 30 sec. how far has it traveled after 30 sec? Distance and speed. A bicyclist decelerates at a constant rate from 30km/hr to a complete stop in 45 sec. a. How fast is the bicyclist traveling after 20 sec? b. How far has the bicyclist traveling after 45sec?84. Distance and speed. A cheetah decelerates at a constant rate from 50km/hr to a complete stop in 20 sec. a. How fast is the cheetah moving after 10 sec? b. How far has the cheetah traveled after 20sec? Distance. For a freely falling object, a(t)=32ft/sec?,v(0)=intialvelocity=v0(inft/sec),ands(0)=intialheight=s0(inft). Find a general expression for s(t) in terms of v0ands0. s(t)=16t2+v0t+s0 Time. A ball is thrown upward from a height of 10 ft, that is, s(0)=10, at an initial velocity of 80ft/sec,orv(0)=80. How long will it take before the ball hits the ground? (See Exercises 85.)87E 88. Distance. A motorcycle accelerates at a constant rate from 0 to 50mph in 15 sec. How far does it travel during that time? 89. Physics. A particle starts at the origin. Its velocity, in miles per hour, after t hours is given by . How far does it travel from the start of the 2nd hour through the end of the 5th hour ? 90E Total pollution. A factory is polluting a lake in such a way that the rate of pollution entering the take after t months is N(t)=280t3/2, Where N(t) is the total number of pounds of pollutions in the lake after t months. How many pounds of pollutions enter the lake in 16 months? b. An environmental board tells the factory that it must begin cleanup procedures after 50,000lb of pollutants have entered the lake. After what length of time will this occur?Accumulated sales. Bluetape, Inc., estimates that is sales are growing continuously at a rate given by S(t)=0.5et, Where S(t) is in dollars per day, on day t. on what day will accumulated sales first exceed $10,000?93E 94E Evaluate. 416(x1)xdx 96E 97E 98E 99E Evaluate. 49t+1tdt 101E Explain the error that has been made in each of Exercises 101 and 102. 12(Inxex)dx=[1xex]12 =(12e2)(1e1)=ee212 103E 104E 105E 106E Evaluate. Prove that abf(x)dx=baf(x)dx Find the area under the graph of over. 1. Find the area under the graph of f over [1,5]. f(x)={x+5,forx4,1112x,forx4 Find the area under the graph of over. 3. Find the area under the graph of g over [2,3]. g(x)={x2+5,forx0,x+5,forx0 Find the area under the graph of f over [6,4]. f(x)={x26x+7,forx1,32x1,forx1 Find the area under the graph of f over [6,4]. f(x)={x1,forx1,x2+4x+5,for1 Find the area represented by each definite integral. 04|x3|dx Find the area represented by each definite integral. 11|3x2|dx Find the area represented by each definite integral. 02|x31|dx Find the area represented by each definite integral. 34|x3|dx Find the area of the shaded region. f(x)=2x+x2x3,g(x)=0 Find the area of the shaded region. 12. Find the area of the shaded region. 13. Find the area of the shaded region. 14. Find the area of the region bounded by the graphs of the given equations. y=x,y=x2,x=0,x=1 Find the area of the region bounded by the graphs of the given equations. y=x,y=x4 Find the area of the region bounded by the graphs of the given equations. y=x+2,y=x2 Find the area of the region bounded by the graphs of the given equations. 18. Find the area of the region bounded by the graphs of the given equations. y=6xx2,y=x Find the area of the region bounded by the graphs of the given equations. y=x26x,y=x Find the area of the region bounded by the graphs of the given equations. y=2xx2,y=x Find the area of the region bounded by the graphs of the given equations. 22. Find the area of the region bounded by the graphs of the given equations. 23. 24E Find the area of the region bounded by the graphs of the given equations. 25. 26E Find the area of the region bounded by the graphs of the given equations. y=4x2,y=44x Find the area of the region bounded by the graphs of the given equations. y=x2+1,y=x2,x=1,x=3 Find the area of the region bounded by the graphs of the given equations. y=x2+3,y=x2,x=1,x=2 Find the area of the region bounded by the graphs of the given equations. f(x)=x2x5,g(x)=x+10 Find the area of the region bounded by the graphs of the given equations. 31. Find the area of the region bounded by the graphs of the given equations. 32. Find the area of the region bounded by the graphs of the given equations. y=2x26x+5,y=x2+6x15 Find the average function value over the given interval. y=2x3;[1,1]Find the average function value over the given interval. y=4x2;[2,2]Find the average function value over the given interval. y=ex;[0,1]Find the average function value over the given interval. 37. Find the average function value over the given interval. y=x2x+1;[0,2]Find the average function value over the given interval. 39. Find the average function value over the given interval. f(x)=mx+1;[0,2]Find the average function value over the given interval. f(x)=4x+5;[0,a]Find the average function value over the given interval. f(x)=xn,n0;[0,1]Find the average function value over the given interval. 43. Find the average function value over the given interval. 44. 45. Total and average daily profit. Shylls, Inc., determines that its marginal revenue per day is given by , where is the total accumulated revenue, in dollars, on the day. The company’s marginal cost per day is given by , where is the total accumulated cost, in dollars, on the day. a. Find the total profit from (the first 10 days). . b. Find the average daily profit for the first 10 days. 46. Total and average daily profit. Great Green, Inc., determines that its marginal revenue per day is given by , Where is the total accumulated revenue, in dollars, on the day. The company’s marginal cost per day is given by , where is the total accumulated cost, in dollars, on the day a. Find the total profit from (see Exercise 45). b. Find the average daily profit for the first 10 days. 47. Accumulated sales. ProArt, Inc., estimates that its weekly online sales, , in hundreds of dollars, t weeks after online sales began, is given by . Find the average weekly sales for the first 5 weeks after online sales began. Accumulated sales. Music Manager, Ltd., estimates that monthly revenue, R(t), in thousands of dollars, attributable to its site t months after the site was launched, is given by R(t)=0.5et. Find the average monthly revenue attributable to the Web site for its first 4 months of operation. 6699.77 Refer to Exercise 47. Find ProArts average weekly online sales for weeks 2 through 5(t=1tot=5).Refer to Exercise 48. Find the average monthly revenue from Music Managers Web site for months 3 through 5(t=2tot=5).Memorizing. In a memory experiment, Alan is able to memorize words at the rate (in words per minute) given by m(t)=0.009t2+0.2. In the same memory experiment, Bonnie is able to memorize words at the rate given by M(t)=0.003t2+0.2t. a. How many more words does the person whose memorization rate is higher memorize from t=0tot=10 (during the first 10 min of the experiment)? b. Over the first 10 min of the experiment, on average, how many words per minute did Alan memorize? c. Over the first 10 min of the experiment, on average, how many words per minute did Bonnie memorize?Results of studying. Celias score on a test, s(t), after t hours of studying, is given by s(t)=t2,0t10, Dans score on the same test is given by S(t)=10t,0t10, where S(t) is his score after t hours of studying. a. For 0t10, who will have the higher test score? b. Find the average value of s(t) over [7,10], and explain what it represents. c. Find the average value of S(t) over [6,10], and explain what it represents. d. Assuming that both students have the same study habits and are equally likely to study for any number of hours, t, in [0, 10][0, 10], on average, how far apart will their test scores be?Results of practice. A keyboarders speed over a 5-min interval is given by W(t)=6t2+12t+90,tin[0,5], where W(t) is the speed, in words per minute, at time t. a. Find the speed at the beginning of the interval. b. Find the maximum speed and when it occurs. c. Find the average speed over the 5-min interval.54. Average population. The population of the United States can be approximated by , where is in millions and t is the number of years since 2000. (Source: Population Division, U.S. Census Bureau.) Find the average value of the population from 2009 to 2013. 55. Average drug dose. The concentration, , of phenylbutazone, in micrograms per milliliter (μg/mL), in the plasma of a calf injected with this anti-inflammatory agent is approximately , where t is the number of hours after the injection and. (Source: A. K. Arifah and P. Lees, “Pharmacodynamics and Pharmacokinetics of Phenylbutazone in Calves,” Journal of Veterinary Pharmacology and Therapeutics, Vol. 25, 299–309 (2002).) a. Given that this model is accurate for, what is the initial dosage? b. What is the average amount of phenylbutazone in the calf’s body for the time between 10 and 120 hours? New York temperature. For any date, the average temperature in New York can be approximated by T(x)=43.518.4x+8.57x20.996x3+0.0338x4, where T represents the temperature in degrees Fahrenheit, x=1 represents the middle of January, x=2 represents the middle of February, and so on. (Source: Based on data from www.worldclimate.com.) Compute the average temperature in New York over the whole year to the nearest degree.57. Outside temperature. Suppose the temperature in degrees Celsius over a 10-hr period is given by . a. Find the average temperature. b. Find the minimum temperature. c. Find the maximum temperature. 58. Engine emissions. The emissions of an engine are given by , where is the engine’s rate of emission, in billions of pollution particulates per year, at time t, in years. Find the average emissions from. 59E 60E 61E 62E 63E 64E 65. Find the area bounded by, the x-axis, and the first coordinates of the relative maximum and minimum values of the function. 66. Life science: Poiseuille’s Law. The flow of blood in a blood vessel is faster toward the center of the vessel and slower toward the outside. The speed of the blood is given by , where R is the radius of the blood vessel, r is the distance of the blood from the center of the vessel, and p, v, and L are physical constants related to the pressure and viscosity of the blood and the length of the blood vessel. If R is constant, we can regard V as a function of r: . The total blood flow, Q, is given by . Find Q. 67E Find the area of the region enclosed by the given graphs. y=x2+4x,y=16x2 Find the area of the region enclosed by the given graphs. 69. Find the area of the region enclosed by the given graphs. 70. 71E 72. Consider the following functions: a. Graph f and g in the window, with Yscl=10. b. Estimate the first coordinates a, b, and c of the three points of intersection of the two graphs. c. Find the area between the curves over . d. Find the area between the curves over Evaluate. (Be sure to check by differentiating!) 1. Evaluate. (Be sure to check by differentiating!) (x27)62xdx Evaluate. (Be sure to check by differentiating!) 3. Evaluate. (Be sure to check by differentiating!) 4. Evaluate. (Be sure to check by differentiating!) 5. Evaluate. (Be sure to check by differentiating!) (2t53)t4dt Evaluate. (Be sure to check by differentiating!) 7. Evaluate. (Be sure to check by differentiating!) 55x+7dx Evaluate. (Be sure to check by differentiating!) 9. Evaluate. (Be sure to check by differentiating!) 10. Evaluate. (Be sure to check by differentiating!) e3xdx Evaluate. (Be sure to check by differentiating!) e7xdx Evaluate. (Be sure to check by differentiating!) 13. Evaluate. (Be sure to check by differentiating!) ex/2dx Evaluate. (Be sure to check by differentiating!) x4ex5dx Evaluate. (Be sure to check by differentiating!) 16. Evaluate. (Be sure to check by differentiating!) 17. Evaluate. (Be sure to check by differentiating!) t2et3dt Evaluate. (Be sure to check by differentiating!) 19. Evaluate. (Be sure to check by differentiating!) 20. Evaluate. (Be sure to check by differentiating!) 21. Evaluate. (Be sure to check by differentiating!) 22. Evaluate. (Be sure to check by differentiating!) 23. Evaluate. (Be sure to check by differentiating!) dx4x Evaluate. (Be sure to check by differentiating!) t(t21)5dt Evaluate. (Be sure to check by differentiating!) t2(t31)7dt Evaluate. (Be sure to check by differentiating!) 27. Evaluate. (Be sure to check by differentiating!) 28. Evaluate. (Be sure to check by differentiating!) exdx4+ex Evaluate. (Be sure to check by differentiating!) 30. Evaluate. (Be sure to check by differentiating!) 31. (Hint: Use the properties of logarithms.) Evaluate. (Be sure to check by differentiating!) 32. Evaluate. (Be sure to check by differentiating!) 33. Evaluate. (Be sure to check by differentiating!) dxxInx2,x1 Evaluate. (Be sure to check by differentiating!) xax2+bdx Evaluate. (Be sure to check by differentiating!) ax+bdx Evaluate. (Be sure to check by differentiating!) P0ektdt Evaluate. (Be sure to check by differentiating!) beaxdx Evaluate. (Be sure to check by differentiating!) 39. Evaluate. (Be sure to check by differentiating!) 3x2dx(1+x3)5 Evaluate. (Be sure to check by differentiating!) 12x1+6x25dx Evaluate. (Be sure to check by differentiating!) 42. 43E 44E Evaluate. 01x(x2+1)5dx Evaluate. 46. Evaluate. 04dt1+t 48E Evaluate. 142x+1x2+x1dx Evaluate. 50. 51E 52E 53E 54E Evaluate. 55. Evaluate. 56. Evaluate. 023x2dx(1+x3)5 Evaluate. 58. Evaluate. 077x1+x23dx 60E a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 012xex2dx a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 013x2ex3dx a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 01x(x2+1)5dx a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 12x(x21)7dx a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 04dt1+t a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 66. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 67. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 68. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 69. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 0b2e2xdx a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 71. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 72. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 04(x6)2dx a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 74. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 75. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 76. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 77. a. 61-78. Use a graphing calculator to check the results of Exercises 43-60. Left to the student Evaluate. Use the technique of Example 9. 0112x1x25dx Evaluate. Use the technique of Example 9. xx5dx Evaluate. Use the technique of Example 9. 3x2x+1dx Evaluate. Use the technique of Example 9. 81. Evaluate. Use the technique of Example 9. x+3x2dx (Hint: u=x2. )Evaluate. Use the technique of Example 9. 2x+33x2dx Evaluate. Use the technique of Example 9. x2(x+1)10dx Evaluate. Use the technique of Example 9. 85. Evaluate. Use the technique of Example 9. 86. Demand from marginal demand. Masterson Insoles, Inc., has the marginal-demand function D(x)=2000x25x2, D(x)=20025x2+5000 Where D(x) is the number of units sold at x dollars per unit. Find the demand function given that D=13,000whenx=3 per unit.Profit from marginal profit. A firm has the marginal-profit function dPdx=90003000x(x26x+10)2, Where P(x) is the profit earned at x dollars per unit. Find the total-profit function given that P=1500atx=3.Marginal rate. The marriage rate in the United states is approximated by M(t)=8.3e0.019t Where M(t) is the number of marriage per 1000 people, t years after 2000. (Source: Based on data from www.cdc.gov.) Find the total number of marriage per 1000 people in the United States from 2000 to 2005.note that this is given by 05M(t)dt Find the total number of marriage per 1000 people in the United States between 2005 and 2016.Divorce rate. The divorce rate in the United States is approximated by D(t)=3.95e0.012t Where D(t) is the number of marriage per 1000 people, t years after 2000. (Source: Based on data from www.cdc.gov.) Find the total number of divorces per 1000 people in the United States from 2000 to 2008. Note that this is given by 08D(t)dt b. Find the total number of divorces in the United States between 2008 and 2006.Find the total area of the shaded region. 91. Find the total area of the shaded region.Evaluate. 93. 94E Evaluate. 95. 96E Evaluate. e1/tt2dt 98E 99E Evaluate. 100. 101E 102E 103E 104E 105E 106E 107E 108E 109E 110E Evaluate. 111. Evaluate. exexex+exdx 113E 114E 115E 116E 117. Is the following a true statement? Why or why not? Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 1. Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 2. Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 3. Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 4. Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 5. Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 6. Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. xe2xdx Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 8. Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 9. Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. x3Inxdx Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 11. Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. x2Inx3dx Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. In(x+5)dx Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 14. Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 15. Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 16. Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. (x1)Inxdx Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 18. Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. xx+2dx Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 20. Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 21. Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. x2In(5x)dx Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. x2exdx Evaluate using integration by parts or substation. (Assume in u.) Check by differentiating. 24. Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. x2e2xdx Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. x5Inxdx Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. x3e2xdx Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. x5e4xdx 29E Evaluate using integration by parts or substation. (Assume u0 in u.) Check by differentiating. (x3x+1)exdx Evaluate using integration by parts. 31. Evaluate using integration by parts. 32. Evaluate using integration by parts. 33. Evaluate using integration by parts. 05In(x+7)dx Evaluate using integration by parts. 01xexdx Evaluate using integration by parts. 36. Evaluate using integration by parts. 08xx+1dx 38E 39E Profit from marginal profit. Nevin Patio Contractions determines that its marginal-profit function is given by P(x)=1000x2e0.2x P(x)=5000x2e0.2x50,000xe0.2x250,000e0.2x+248,000 Find the total profit given that P(0)=2000.41. Drug dosage. Suppose an oral dose of a drug is taken. Over time, the drug is assimilated in the body and excreted in the urine. The total amount of the drug that passes through the body in T hours is given by Where E is the rate of excretion of the drug. A typical rate-of-excretion function is , Where and t is the time, in hours. Find a formula for . Find . Electrical energy use. The rate at which electrical energy is used by the Ortiz family, in kilowatt-hours (kW-h) per day, is given by K(t)=10tet, where t is time, in hours. That is, t in the interval [0,24]. 10TeT10T+10 a. How many kilowatt-hours does the family use in the first T house of a day (t=0tot=T)? b. How many kilowatt-hours does the family use in the first 4 house of a day?In Exercises 43-44, evaluate the given indefinite interval using substitution. Refer to Example 9 in section 4.5 to review the technique. 43. Evaluate by letting and observing that. Compare your answer to that found in Exercises 3 of this section. Are they the same? (Hint: Simplify both forms of the answer into a common third form.) In Exercises 43-44, evaluate the given indefinite interval using substitution. Refer to Example 9 in section 4.5 to review the technique. Consider xx3dx. a. Evaluate this integral using integration by parts. b. Evaluate this integral using the substitution u=x3 and observing that x=u+3. c. Show algebraically that the answer from parts (a) and (b) are equivalent.45E 46E 47E Evaluate. tet(t+1)2dt 49E 50E 51E 52E 53E Evaluate. xnInxdx,n1 55E 56. Verify that for any positive integral n, . 57. Is the following a true statement? . Why or why not? 58E Occasionally, integration by parts yields an integral of the form udv that is identical to the original. In some cases, we can then solve for udv algebraically. For example, to find 2xexweLetu=2xanddv=exsodu=(In2)2xdxandv=ex. Using integral by parts, we have 2xexdx=2xexIn22xexdx. Note that 2xexdx appears twice. Adding In22xexdx to both sides, we have 2xexdx+In22xexdx=2xex (1+In2)2xexdx=2xex 2xexdx=2xex1+In2+C. Use this method to evaluate the integrals in Exercises 59-62. 3xexdx 60E Occasionally, integration by parts yields an integral of the form udv that is identical to the original. In some cases, we can then solve for udv algebraically. For example, to find 2xexweLetu=2xanddv=exsodu=(In2)2xdxandv=ex. Using integral by parts, we have 2xexdx=2xexIn22xexdx. Note that 2xexdx appears twice. Adding In22xexdx to both sides, we have 2xexdx+In22xexdx=2xex (1+In2)2xexdx=2xex 2xexdx=2xex1+In2+C. Use this method to evaluate the integrals in Exercises 59-62. 10xe3xdx 62E 63E Find each antiderivative using Table 1. xe3xdx Find each antiderivative using Table 1. 2xe3xdx 3E

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