(a) Explanation Given Information: The revenue of product in millions of dollars is modelled as R = 144 t 2 + 400 . Formula used: The formula for integral ∫ u 2 ± a 2 d u is, ∫ u 2 ± a 2 d u = 1 2 ( u u 2 ± a 2 ± a 2 ln | u + u 2 ± a 2 | ) + C Calculation: Let u = 12 t . Differentiate the above function with respect to x , d u = 12 d t Consider the provided expression, R = 144 t 2 + 400 Integrate the above function with lower limit as 0 and higher limit as 3 in order to total revenue of the product during first three years on market, which can be written as, R = ∫ 0 3 144 t 2 + 400 d t Rewrite. R = ∫ 0 3 ( 12 t ) 2 + 20 2 d t Multiply and divide by 12 . R = 1 12 ∫ 0 3 12 ( 12 t ) 2 + 20 2 d t = 1 12 ∫ 0 3 ( ( 12 t ) 2 + 20 2 ) 12 d t Here, a = 20 , u = 12 t and d u = 12 d t . Substitute u for 12 t , a for 20 , and d u for 12 d t . R = 1 12 ∫ 0 3 u 2 + a 2 d u Use the formula 23 and solve the above integral as: R = 1 12 [ 1 2 ( u u 2 + a 2 + a 2 ln | u + u 2 + a 2 | ) ] 0 3 Substitute 12 t for u , and 20 for a (b) To determine To calculate: The total revenue of the product during first six years on market, when the revenue of product in millions of dollars is modelled as R = 144 t 2 + 400 .

Calculus: An Applied Approach (Providence College: MTH 109)

9th Edition

ISBN: 9781285142616

Author: Ron Larson

Publisher: CENGAGE C

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Chapter 6.2, Problem 15QY

(a)

To determine

To calculate: The total revenue of the product during first three years on market, when the revenue of product in millions of dollars is modelled as R=144t2+400.

(b)

To determine

To calculate: The total revenue of the product during first six years on market, when the revenue of product in millions of dollars is modelled as R=144t2+400.

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Chapter 6.2, Problem 14QY

Chapter 6.2, Problem 16QY

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Calculus: An Applied Approach (Providence College: MTH 109)

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The total revenue of the product during first three years on market, when the revenue of product in millions of dollars is modelled as R = 144 t 2 + 400 .

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