Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Calculus: An Applied Approach (MindTap Course List)
23E24EEvaluating a Definite Integral In Exercises 17-38, evaluate the definite integral. See Examples 3 and 4. 11(t32)dt26EEvaluating a Definite Integral In Exercises 17-38, evaluate the definite integral. See Examples 3 and 4. 10(t1/3t2/3)dt28EEvaluating a Definite Integral In Exercises 17-38, evaluate the definite integral. See Examples 3 and 4. 283xdx30EEvaluating a Definite Integral In Exercises 17-38, evaluate the definite integral. See Examples 3 and 4. 0412x+1dxEvaluating a Definite Integral In Exercises 17-38, evaluate the definite integral. See Examples 3 and 4. 02x1+2x2dx33EEvaluating a Definite Integral In Exercises 17-38, evaluate the definite integral. See Examples 3 and 4. 11(exex)dxEvaluating a Definite Integral In Exercises 1738, evaluate the definite integral. See Examples 3 and 4. 01e2xe2x+1dxEvaluating a Definite Integral In Exercises 1738, evaluate the definite integral. See Examples 3 and 4. 03exex+1dx37E38EDefinite Integral Involving Absolute Value In Exercises 39-42, evaluate the definite integral. See Example 5. 21|4x|dxDefinite Integral Involving Absolute Value In Exercises 39-42, evaluate the definite integral. See Example 5. 13| x3 |dxDefinite Integral Involving Absolute Value In Exercises 39-42, evaluate the definite integral. See Example 5. Definite Integral Involving Absolute Value In Exercises 39-42, evaluate the definite integral. See Example 5. 28|3x9|dx42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62EIntegrating Even and Odd Functions In Exercises 6164, evaluate the definite integral using the properties of even and odd functions. See Example 8. 11(2t52t)dt64EUsing Properties of Definite Integrals Use the value 01x2dx=13 to evaluate each definite integral. Explain your reasoning. (a) 10x2dx(b)11x2dx(c)01x2dx66EFinding the Amount of an Annuity In Exercises 67-70, find the amount of an annuity with income function C(t), interest rate r, and term T. See Example 9. c(t)=250,r=8,T=6years68EFinding the Amount of an Annuity In Exercises 67-70, find the amount of an annuity with income function C(t), interest rate r, and term T. See Example 9. c(t)=1500,r=2,T=10years70ECapital Accumulation In Exercises 71-74, you are given the rate of investment dI/dt. Find the capital accumulation over a five-year period by evaluating the definite integral Capital accumulation =05dIdtdt where t is the time (in years). dIdt=50072E73ECapital Accumulation In Exercises 71-74, you are given the rate of investment dl/dt. Find the capital accumulation over a five-year period by evaluating the definite integral Capital accumulation 05dldtdt where t is the time (in years). dIdt=12,000t(t2+2)2Cost The total cost of purchasing a piece of equipment and maintaining it for x years can be modeled by C=5000(25+30xt1/4dt) Find the total cost after (a) 1 year, (b) 5 years, and (c) 10 years.Depreciation A company purchases a new machine for which the rate of depreciation can be modeled by dvdt=10,000(t6),0t5 where V is the value of the machine after t years. Set up and evaluate the definite integral that yields the total loss of value of the machine over the first 3 years.77EHOW DO YOU SEE IT? A college graduate has two job offers. The starting salary for each is $32,000, and after 8 years of service each will pay $54,000. The salary increase for each offer is shown in the figure. From a strictly monetary viewpoint, which is the better offer? Explain your reasoning.Mortgage Debt The rate of change of mortgage debt outstanding for one- to four-family homes in the United States from 2000 through 2013 can be modeled by dMdt=1.079+2.555t0.50.75428t+0.0000061etdt where M is the mortgage debt outstanding (in trillions of dollars) and t is the year, with t = 0 corresponding to 2000. In 2000, the mortgage debt outstanding in the United States was $5.1 trillion. (Source: Board of Governors of the Federal Reserve System) (a) Write a model for the debt as a function of t. (b) What was the average mortgage debt outstanding for 2000 through 2013?Checkpoint 1 Worked-out solution available at LarsonAppliedCalculus.com Find the area of the region bounded by the graphs of y=x2+1andy=xfor0x2. Sketch the region bounded by the graphs.2CP3CP4CP5CP6CP1SWU2SWU3SWU4SWU5SWU6SWU7SWU8SWUFinding the Area Bounded by Two Graphs In Exercises 1-8, find the area of the region. See Examples 1, 2, 3, and 4. f(x)=x26xg(x)=02EFinding the Area Bounded by Two Graphs In Exercises 1-8, find the area of the region. See Examples 1, 2, 3, and 4. f(x)=x24x+3g(x)=x2+2x+34EFinding the Area Bounded by Two Graphs In Exercises 1-8, find the area of the region. See Examples 1, 2, 3, and 4. f(x)=ex1g(x)=06E7EFinding the Area Bounded by Two Graphs In Exercises 1-8, find the area of the region. See Examples 1, 2, 3, and 4. f(x)=(x1)3g(x)=x19E10E11E12E13E14EFinding the Area Bounded by Two Graphs In Exercises 15-30, sketch the region bounded by the graphs of the functions and find the area of the region. See Examples 1, 2, 3, and 4. y=x21,y=x+2,x=0,x=116EFinding the Area Bounded by Two Graphs In Exercises 15-30, sketch the region bounded by the graphs of the functions and find the area of the region. See Examples 1, 2, 3, and 4. y=x24x+3,y=3+4xx218E19E20E21E22EFinding the Area Bounded by Two Graphs In Exercises 15-30, sketch the region bounded by the graphs of the functions and find the area of the region. See Examples 1, 2, 3, and 4. f(x)=x3+4x2,g(x)=x+424E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42EConsumer and Producer Surpluses In Exercises 43-48, find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). See Example 5. Demand Function Supply Function p=500.5xp=0.125xConsumer and Producer Surpluses In Exercises 43-48, find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). See Example 5. Demand Function Supply Function p=300xp=100+xConsumer and Producer Surpluses In Exercises 43-48, find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). See Example 5. Demand Function Supply Function p=2000.4xp=100+1.6xConsumer and Producer Surpluses In Exercises 43-48, find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). See Example 5. Demand Function Supply Function p=97523xp=42xConsumer and Producer Surpluses In Exercises 43-48, find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). See Example 5. Demand Function Supply Function p=420.015x2p=0.01x2+248ERevenue In Exercises 49 and 50, two models, R1 and R2, are given for revenue (in billions of dollars) for a large corporation. Both models are estimates of revenues for 2020 through 2025, where t = 20 corresponds to 2020. Which model projects the greater revenue? How much more total revenue does that model project over the six-year period? R1=7.21+0.58t,R2=7.21+0.45tRevenue In Exercises 49 and 50, two models, R1 and R2, are given for revenue (in billions of dollars) for a large corporation. Both models are estimates of revenues for 2020 through 2025, where t = 20 corresponds to 2020. Which model projects the greater revenue? How much more total revenue does that model project over the six-year period? R1=7.21+0.26t+0.02t2,R2=7.21+0.1t+0.01t2Fuel Cost The projected fuel cost C (in millions of dollars) for an airline from 2020 through 2030 is C1=568.5+7.15t where t = 20 corresponds to 2020. After purchasing more efficient airplane engines, the fuel cost is expected to decrease and to follow the model C2=525.6+6.43t. How much money will the airline save with the more efficient engines? Explain your reasoning.Health An epidemic was spreading such that t weeks after its outbreak it had infected N1(t)=0.1t2+0.5t+150,0t50 people. Twenty-five weeks after the outbreak, a vaccine was developed and administered to the public. At that point, the number of people infected was governed by the model N2(t)=0.2t2+6t+200. Approximate the number of people that the vaccine prevented from becoming ill during the epidemic.53EHOW DO YOU SEE IT? A state legislature is debating two proposals for eliminating the annual budget deficits after 10 years. The rate of decrease of the deficits for each proposal is shown in the figure. (a) What does the area between the two graphs represent? (b) From the viewpoint of minimizing the cumulative state deficit, which is the better proposal? Explain your reasoning.55E56EConsumer and Producer Surpluses Factory orders for an air conditioner are about 6000 units per week when the price is $331 and about 8000 units per week when the price is $303. The supply function is given by p=0.0275x. Find the consumer and producer surpluses. (Assume the demand function is linear.)Consumer and Producer Surpluses Repeat Exercise 57 with a demand of about 6000 units per week when the price is $325 and about 8000 units per week when the price is $300. Find the consumer and producer surpluses. (Assume the demand function is linear.)1CP2CP3CP1SWU2SWU3SWU4SWU5SWU6SWU7SWU8SWU9SWU10SWUApproximating the Area of a Plane Region In Exercises 1-6, use the rectangles to approximate the area of the region. Compare your result with the exact area obtained using a definite integral. See Example 1. f(x)=x+3,[1,3]2E3E4E5EApproximating the Area of a Plane Region In Exercises 1-6, use the rectangles to approximate the area of the region. Compare your result with the exact area obtained using a definite integral. See Example 1. f(x)=ex/2,[0,3]7E8E9E10E11E12E13E14E15E16E17E18E19E20ESurface Area Use the Midpoint Rule to estimate the surface area of the pond shown in the figure.Surface Area Use the Midpoint Rule to estimate the surface area of the golf green shown in the figure.31E33E1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14REFinding Present Value In Exercises 1316, find the present value of the income c (in dollars) over t1 years at the given annual inflation rate r. c=24,000t,r=5,t1=10years16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60REEndowment In Exercises 61 and 62, determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate r compounded continuously. P=8000,r=362RE63RE64RE1TYS2TYS3TYS4TYS5TYS6TYS7TYS8TYS9TYS10TYS11TYS12TYS13TYS14TYS15TYS16TYS17TYS18TYS1CP2CP3CP4CP5CP6CP7CP1SWU2SWU3SWU4SWU5SWU6SWU7SWU8SWU9SWU10SWU1E2E3E4EIntegration by Parts In Exercises 5-16, use integration by parts to find the indefinite integral. See Examples 1, 2, 3, and 4. xe3xdx6EIntegration by Parts In Exercises 5-16, use integration by parts to find the indefinite integral, See Examples 1, 2, 3, and 4. x3lnxdx8EIntegration by Parts In Exercises 5-16, use integration by parts to find the indefinite integral, See Examples 1, 2, 3, and 4. ln5xdx10EIntegration by Parts In Exercises 5-16, use integration by parts to find the indefinite integral, See Examples 1, 2, 3, and 4. x2exdx12EIntegration by Parts In Exercises 5-16, use integration by parts to find the indefinite integral, See Examples 1, 2, 3, and 4. x2x+4dx14EIntegration by Parts In Exercises 5-16, use integration by parts to find the indefinite integral, See Examples 1, 2, 3, and 4. x2(lnx)3dx16E17E18E19E20EFinding an Indefinite Integral In Exercises 17-38, find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) x2ex/4dxFinding an Indefinite Integral In Exercises 17-38, find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) 32x2ex/2dx23E24EFinding an Indefinite Integral In Exercises 17-38, find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) e1/tt2dt26E27E28E29E30E31E32E33E34E35E