(a) Explanation Given: The provided function, L ' ( t ) = 70 ln ( t + 1 ) t + 1 where t the time in hours. Formula used: ∫ a b f ( x ) d x = F ( b ) − F ( a ) Calculation: Consider the function, L ' ( t ) = 70 ln ( t + 1 ) t + 1 As the tanker hits a hidden rock when t = 0 . To obtain the total number of barrels leak on the first day then the limits will be from t = 0 to t = 24 hours that is given in the form of a definite integral. ∫ 0 24 L ' ( t ) = ∫ 0 24 70 ln ( t + 1 ) t + 1 Use fundamental theorem of the definite integral. ∫ f ( x ) a b = f ( b ) − f ( a ) Then use the substitution method, ln ( t + 1 ) = x …… (1) Then its derivative is: 1 t + 1 d t d x = 1 1 t + 1 d t = d x Therefore, 1 t + 1 d t = d x …… (2) Now substitute equation (1) and (2) in the above function (b) To determine To calculate: The total number of barrels that the ship will leak on the second day. (c) To determine When the amount of oil leaked per day over the long run.

12th Edition

ISBN: 9780135240687

Author: Lial

Publisher: PEARSON

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Chapter 13.5, Problem 59E

(a)

To determine

To calculate: The total number of barrels that the ship will leak on the first day.

(b)

To determine

To calculate: The total number of barrels that the ship will leak on the second day.

(c)

To determine

When the amount of oil leaked per day over the long run.

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Chapter 13.5, Problem 58E

Chapter 13.5, Problem 60E

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