(a) Explanation Given Information: The demand of the product over next five years is modelled as x = 1000 ( 45 + 20 t e − 0.5 t ) for 0 ≤ t ≤ 5 . Formula used: The formula for integration by parts is, ∫ u d v = u v − ∫ v d u Here, u and v be the differentiable functions x . Integral Rule of exponential function: ∫ e n u d u = e n u n + C Here, n is the any number. Calculation: Consider the provided integral, x = 1000 ( 45 + 20 t e − 0.5 t ) Integrate the above function from lower limit as 0 and higher limit as 5 in order to find the total demand over next five years. x = ∫ 0 5 1000 ( 45 + 20 t e − 0.5 t ) d t Rewrite. x = 1000 ∫ 0 5 ( 45 ) d t + 1000 ∫ 0 5 ( 20 t e − 0.5 t ) d t = 45000 ∫ 0 5 d t + 20000 ∫ 0 5 ( t e − 0.5 t ) d t Let u = t and d v = e − 0.5 t d t . So, d u = d t And, v = ∫ d v = ∫ e − 0.5 t d t = e − 0.5 t − 0.5 = − 2 e − 0.5 t Apply integration by parts and power rule of integration to solve integral of 45000 ∫ 0 5 d t + 20000 ∫ 0 5 ( t e − 0 (b) To determine To calculate: The average annual demand during five years, when demand of the product over next five years is modelled as x = 1000 ( 45 + 20 t e − 0.5 t ) for 0 ≤ t ≤ 5 .

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.2, Problem 7QY

(a)

To determine

To calculate: The total demand over next five years, when demand of the product over next five years is modelled as x=1000(45+20te−0.5t) for 0≤t≤5.

(b)

To determine

To calculate: The average annual demand during five years, when demand of the product over next five years is modelled as x=1000(45+20te−0.5t) for 0≤t≤5.

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Chapter 6.2, Problem 6QY

Chapter 6.2, Problem 8QY

Chapter 6 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 6.1 - Prob. 1CP Ch. 6.1 - Prob. 2CP Ch. 6.1 - Prob. 3CP Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 7CP Ch. 6.1 - Prob. 1SWU Ch. 6.1 - Prob. 2SWU Ch. 6.1 - Prob. 3SWU

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The total demand over next five years, when demand of the product over next five years is modelled as x = 1000 ( 45 + 20 t e − 0.5 t ) for 0 ≤ t ≤ 5 .

Solution Summary: The author explains how to calculate the total demand over next five years.