1 Preliminaries 2 Functions, Limits, And The Derivative 3 Differentiation 4 Applications Of The Derivative 5 Exponential And Logarithmic Functions 6 Integration 7 Additional Topics In Integration 8 Calculus Of Several Variables A Appendix A B Appendix B expand_more
6.1 Antiderivatives And The Rules Of Integration 6.2 Integration By Substitution 6.3 Area And The Definite Integral 6.4 The Fundamental Theorem Of Calculus 6.5 Evaluating Definite Integrals 6.6 Area Between Two Curves 6.7 Applications Of The Definite Integral To Business And Economics Chapter Questions expand_more
Problem 1CQ: Describe two approaches that are used to evaluate a definite integral using the method of... Problem 2CQ Problem 1E: In Exercises 1-28, evaluate the definite integral. 1. 02x(x31)3dx Problem 2E: In Exercises 1-28, evaluate the definite integral. 2. 02x2(2x31)4dx Problem 3E: In Exercises 1-28, evaluate the definite integral. 3. 01x5x2+4dx Problem 4E: In Exercises 1-28, evaluate the definite integral. 4. 13x3x22dx Problem 5E Problem 6E: In Exercises 1-28, evaluate the definite integral. 6. 15(2x1)5/2dx Problem 7E Problem 8E: In Exercises 1-28, evaluate the definite integral. 8. 02xx2+5dx Problem 9E: In Exercises 1-28, evaluate the definite integral. 9. 13(2x1)4dx Problem 10E: In Exercises 1-28, evaluate the definite integral. 10. 12(2x+4)(x2+4x8)3dx Problem 11E Problem 12E: In Exercises 1-28, evaluate the definite integral. 12. 12(x3+34)(x2+3x)2dx Problem 13E: In Exercises 1-28, evaluate the definite integral. 13. 15xx1dx Problem 14E: In Exercises 1-28, evaluate the definite integral. 14. 14xx+1dx Hint: Let u = x +1. Problem 15E Problem 16E: In Exercises 1-28, evaluate the definite integral. 16. 01exdx Problem 17E Problem 18E: In Exercises 1-28, evaluate the definite integral. 18. 02(etet)dt Problem 19E: In Exercises 1-28, evaluate the definite integral. 19. 11xex2+1dx Problem 20E: In Exercises 1-28, evaluate the definite integral. 20. 14exxdx Problem 21E: In Exercises 1-28, evaluate the definite integral. 21. 361x2dx Problem 22E: In Exercises 1-28, evaluate the definite integral. 22. 01x1+2x2dx Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E: In Exercises 1-28, evaluate the definite integral. 27. 12(2e4x1x2)dx Problem 28E: In Exercises 1-28, evaluate the definite integral. 28. 12lnxxdx Problem 29E Problem 30E: In Exercises 29-34, find the area of the region under the graph of f on [a, b]. 30. f(x) = x3 + x;... Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E: In Exercises 35-44, find the average value of the function f over the indicated interval [a, b]. 35.... Problem 36E: In Exercises 35-44, find the average value of the function f over the indicated interval [a, b]. 36.... Problem 37E Problem 38E Problem 39E Problem 40E: In Exercises 35-44, find the average value of the function f over the indicated interval [a, b]. 40.... Problem 41E: In Exercises 35-44, find the average value of the function f over the indicated interval [a, b]. 41.... Problem 42E Problem 43E Problem 44E Problem 45E: VELOCITY of a Car A car moves along a straight road in such a way that its velocity (in feet per... Problem 46E: Oil PRODUCTION On the basis of a preliminary report by a geological survey team, it is estimated... Problem 47E: NET Investment Flow The net investment flow (rate of capital formation) of the giant conglomerate... Problem 48E: Newtons Law of Cooling A bottle of white wine at room temperature (68F) is placed in a refrigerator... Problem 49E: World PRODUCTION of Coal A study proposed in 1980 by researchers from the major producers and... Problem 50E: Depreciation: Double Declining-Balance Method Suppose a tractor purchased at a price of S60,000 is... Problem 51E: Cell Phone Ad Spending Cell phone ad spending between 2005 (t = 1) and 2011 (t = 7) is given by... Problem 52E: Global Warming The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global... Problem 53E: Projected U.S. Gasoline Usage The White House wants to cut gasoline usage from 140 billion gallons... Problem 54E: U.S. Citizens 65 Years and Older The number of U.S. citizens aged 65 years and older from 1900... Problem 55E: Baseball A batted baseball is subjected to a force whose direction is constant but whose magnitude... Problem 56E: Commercial Vehicle Registrations In a report issued by the Economist Intelligence Unit in 2013, the... Problem 57E: Flow of BLOOD in an Artery According to a law discovered by nineteenth century physician Jean Louis... Problem 58E: Total Knee Replacement Procedures The number of total knee replacement procedures (in millions)... Problem 59E: Concentration of a Drug in the Bloodstream The concentration of a certain drug in a patients... Problem 60E: Seat Belt Use According to the U.S. Department of Transportation, the percentage of drivers using... Problem 61E: AVERAGE Yearly Sales The sales of Universal Instruments in the first t years of its operation are... Problem 62E: CABLE TV SUBSCRIBERS The manager of TeleStar Cable Service estimates that the total number of... Problem 63E Problem 64E: U.S. Retail E-Commerce Sales In a 2010 report, U.S. retail e-commerce sales (excluding travel,... Problem 65E: International air Traffic International air traffic in and out of the United States is projected to... Problem 66E: AVERAGE Price OF a Commodity The price of a certain commodity in dollars per unit at time t... Problem 67E Problem 68E: Waste Disposal When organic waste is dumped into a pond, the oxidization process that takes place... Problem 69E Problem 70E: Prove Property 2 of the definite integral. Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E: Verify by direct computation that 01(1+x3)dx=01(1+x3)dx+13(1+x3)dx Problem 76E Problem 77E Problem 78E Problem 81E Problem 82E Problem 83E Problem 84E Problem 85E: In Exercises 81-86, determine whether the statement is true or false. If it is true, explain why it... Problem 86E Problem 1TE Problem 2TE Problem 3TE: In Exercises 1-4, use Property 5 of the definite integral (page 457) to evaluate the definite... Problem 4TE: In Exercises 1-4, use Property 5 of the definite integral (page 457) to evaluate the definite... Problem 5TE: Crop YIELD If left untreated on bean stems, aphids (small insects that suck plant juices) will... Problem 6TE: Absorption OF Drugs Jane took 100 mg of a drug in the morning and another 100 mg of the same drug at... Problem 7TE: Absorption OF DRUGS The concentration of a drug in an organ t seconds after it is administered is... format_list_bulleted