Evaluating definite
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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_forwardEvaluate the definite integral two ways: first by a u-substitution in the definite integral and then by a u-substitution in the corresponding indefinite integral. Enter the exact answer. /2+x dx =arrow_forwardGaussian functions G.1 G.2 G.3 G.4 G.5 G.6 G.7 G.8 8 S 8 0 e-ax² 8 1 [["new" daw ! dx= 0 2a dx= 8 [x²e-dx-1(5) x²e-ax² dx = 4 1 T erfz= 8 S™ 0 11 S x³e-ax² dx= 0 0 2 a 2 3 [x²e-max->()" x¹e-ax² dx= 1 2q² So 1/2 1/2 e-x² dx 1/2 TC¹ m! x² ₂2m+1e¬ax² dx = 2qm+1 x²me-ax² dx = 1/2 erfc z=1-erf z (2m-1)!! T 2m+1 am (2m-1)!!=1×3×5...×(2m-1) (1) a 1/2arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage