Explanation Given Information: The sale for seasonal product is given by expression S = 48.4 − 6.1 cos π t 6 . Formula used: Write the formula for average value of a provided function f ( x ) for [ a , b ] . Average value = 1 b − a ∫ a b f ( x ) d x Write the formula for definite integral of ∫ a b cos n u d u . ∫ a b cos n u d u = [ sin n u n ] a b Here, n is the any number. Write the formula for integral of ∫ a b d u . ∫ a b d u = [ u ] a b Calculation: Consider the sale for seasonal product, S = 48.4 − 6.1 cos π t 6 The average monthly sales in thousands of units during the year 0 ≤ t ≤ 12 cab be calculated by integrating the expression of sale for seasonal product over the interval [ 0 , 12 ] , which can be mathematically written as: average = 1 12 − 0 ∫ 0 12 S d t = 1 12 ∫ 0 12 ( 48.4 − 6.1 cos π t 6 ) d t Rewrite the integral. average = 1 12 { ∫ 0 12 48.4 d t − ∫ 0 12 6.1 cos π t 6 d t } = 1 12 { 48

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 8, Problem 125RE

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To calculate: The average monthly sales in thousands of units during the year 0≤t≤12, when sale for seasonal product is given by expression S=48.4−6.1cosπt6.

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Chapter 8, Problem 124RE

Chapter 8, Problem 126RE

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Calculus: An Applied Approach (MindTap Course List)

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The average monthly sales in thousands of units during the year 0 ≤ t ≤ 12 , when sale for seasonal product is given by expression S = 48.4 − 6.1 cos π t 6 .

Solution Summary: The author calculates the average monthly sales in thousands of units during the year 0le t

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To calculate: The average monthly sales in thousands of units during the year 0≤t≤12, when sale for seasonal product is given by expression S=48.4−6.1cosπt6.

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