Lesson01_-_The_Integral_ws - Worksheet for Section 5.15.5...

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Worksheet for Section 5.1–5.5Review of the Integral, Integration by SubstitutionMATH-UA 122.006: Calculus IISpring 2012The Definite Integral1.The rate at which the world’s oil is being consumed is increasing.Suppose that the rate(measured in billions of barrels per year) is given by the functionr(t), wheretis measured inyears andt= 0 on January 1, 1990.(a) Write a definite integral that represents the total quantity of oil used between the startof 1990 and the start of 1995.(b) Suppose thatr(t) = 32e0.05t. Find the approximate value for the definite integral frompart (a) using a right-hand sum withn= 5 subintervals.(c) Interpret each of the five terms in the sum from part (b) in terms of oil consumption.(d) Evaluate the definite integral from part (a) exactly using the Fundamental Theorem ofCalculus.1

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