Evaluating definite
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Calculus: Early Transcendentals (3rd Edition)
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- Oil Consumption Suppose that the rate of consumption of a natural resource is c(t), where c(t)=kert, Here t is the time in years, r is a constant, and k is the consumption in the year when t=0. In 2010, an oil company sold 1.2 billion barrels of oil. Assume that r=0.04. a. Write c(t) for the oil company, letting t=0 represent 2010. b. Set up a definite integral for the amount of oil that the company will sell in the next 10 years. c. Evaluate the definite integral of part b. d. The company has about 20 billion barrels of oil in reserve. To find the number of years that this amount will last, solve the equation 0T1.2e0.04tdt=20. e. Rework part d, assuming that r=0.02.arrow_forwardUse the total differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the differences in the two results to 4decimal places. 8.052+5.972arrow_forwardThe following integrals may be solved using substitution. Choose a function u that may be used to solve each problem. Then find du. a. (3x25)42xdx b. 1xdx c. x22x3+1dx d. 4x3ex4dxarrow_forward
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