(a) To determine To find: The average intensity of the drug during the second hour where the intensity of the reaction to a drug is given by R ( t ) = t e − 0.1 t where t is time in hours. Explanation Formula used: Average value of a Function: “The average value of a function f on the interval [ a , b ] is 1 b − a ∫ a b f ( x ) d x , provided the indicated definite integral exists”. Integration by parts: “If u and v are differentiable functions, then ∫ u d v = u v − ∫ v d u .” Calculation: The function for the intensity of the reaction to a drug after consumed is given by R ( t ) = t e − 0.1 t where t is time. Find the average intensity of the drug during the n th hour. The time interval during the n th hour is [ n − 1 , n ] . Consider initial stage as a = n − 1 and final stage as b = n . Use the formula for finding the average intensity. The average = 1 b − a ∫ a b f ( x ) d t . = 1 n − ( n − 1 ) ∫ n − 1 n t e − 0.1 t d t = 1 n − n + 1 ∫ n − 1 n t e − 0.1 t d t = ∫ n − 1 n t e − 0.1 t d t Solve the above integral by the method of integration by parts. Let u = t and d v = e − 0.1 t d t . Differentiate u = t as follows. d u d t = 1 d u = d t Integrate d v = e − 0.1 t d t as follows. ∫ d v = ∫ e − 0.1 t d x v = e − 0.1 t − 0.1 v = − 10 e − 0.1 t Substitute the corresponding values in the formula ∫ u d v = u v − ∫ v d u and simplify. ∫ n − 1 n t e − 0.1 t d t = [ t ( − 10 e − 0.1 t ) ] n − 1 n − ∫ n − 1 n ( − 10 e − 0 (b) To determine To find: The average intensity of the drug during the twelfth hour. (c) To determine To find: The average intensity of the drug during the twenty-fourth hour.

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8.2, Problem 41E

(a)

To determine

To find: The average intensity of the drug during the second hour where the intensity of the reaction to a drug is given by R(t)=te−0.1t where t is time in hours.

(b)

To determine

To find: The average intensity of the drug during the twelfth hour.

(c)

To determine

To find: The average intensity of the drug during the twenty-fourth hour.

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Chapter 8.2, Problem 40E

Chapter 8.2, Problem 42E

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Calculus with Applications (11th Edition)

Ch. 8.1 - YOUR TURN 1 Find Ch. 8.1 - YOUR TURN 2 Find Ch. 8.1 - YOUR TURN 3 Find Ch. 8.1 - YOUR TURN 4 Find . Ch. 8.1 - YOUR TURN 5 Find Ch. 8.1 - Prob. 1WE Ch. 8.1 - Find the following. W2. Ch. 8.1 - Find the following. W3. Ch. 8.1 - Find the following. W4. Ch. 8.1 - Use integration by parts to find the integrals in...

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