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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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The sales S (in billions of dollars) for Dollar General from 2008 through 2013 can be modeled by

S = 2.1 t ln t 2 where t is the year, with t = 8 corresponding to 2008. (Source: Dollar General Corporation)

(a) Find the total sales for the years 2008 through 2013.

(b) Find the average sales for the years 2008 through 2013.

(a)

To determine

To calculate: The total sales for the year 2008 through 2013 if the sales is modelled by following function:

s=2.1tlnt2

Where, year 2008 corresponds to t=8.

Explanation

Given Information:

The sales function is provided as:

s=2.1tlnt2

Year 2008 corresponds to t=8.

The total sales between 20018 through 2013 is to be obtained.

Formula used:

The formula for the integration by parts is:

udv=uvvdu

Calculation:

Total sales form the year 2008 through the year 2013 will be the integral of the sales in this time span.

Year 2008 corresponds to t=8 therefore year 2013 will correspond to t=13.

Mathematically, it is expressed as:

total sales=813(2.1tlnt2)dt=8132.1tlntdt8132dt=2.1813tlntdt8132dt

Consider integral:

813tlntdt

Assume dv=t

Integrate,

dv=tdtv=23t3

And assume u=lnt.

Differentiate,

du=1tdt

Use integration by parts to integrate udv=uvvdu

(b)

To determine

To calculate: The average sales for the year 2008 through 2013 if the sales is modelled by following function:

s=2.1tlnt2

Where, year 2008 corresponds to t=8.

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