(a) Explanation Given data: The rate of sales at fireworks outlet is approximately given by f ( x ) = 5 x e − x 3 . Also, at x = 0 , F ( 0 ) = 0 . Formula used: Write the formula used for integration by parts: ∫ p d q = p q − ∫ q d p Here p and q are the functions of x. Calculation: The total sales will be the integral of the rate sales rate of the fireworks. Mathematically, it is expressed by the following expression: F ( x ) = ∫ f ( x ) d x = ∫ 5 x e − x 3 d t Now find ∫ 5 x e − x 3 d x by integrating it by part. Let p = 5 x and d q = e − x 5 d x . Now, d p = 5 d x Find q by integrating d q . d q = e − x 3 d x q = − 3 e − x 3 Ignore the constant of integration in the above integration. Now use the above formula to find ∫ 5 x e − x 3 d x (b) To determine To calculate: The total sales since the start of July through x = 4 .

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ISBN: 9780135335215

Author: Lial

Publisher: PEARSON

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Chapter 13.3, Problem 44E

(a)

To determine

To calculate: The function F(x) that gives total sales since the start of July through day x.

(b)

To determine

To calculate: The total sales since the start of July through x=4.

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Chapter 13.3, Problem 43E

Chapter 13.3, Problem 45E

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The function F ( x ) that gives total sales since the start of July through day x.

Solution Summary: The author calculates the function F(x) that gives total sales since the start of July through day x.