Chapter 5.5, Problem 86E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after *t* weeks is

(Notice that production approaches 5000 per week as time goes on, but the initial production is lower because of the workers’ unfamiliarity with the new techniques.) Find the number of calculators produced from the beginning of the third week to the end of the fourth week.

To determine

**To find:** The number of calculators produced from the beginning of the third week to the end of the fourth week.

Explanation

**Given:**

The rate of production of calculators is represents as a function as follows:

**Calculation:**

Show the integral function after applying the limits.

The region lies between

Consider

Differentiate both sides of the Equation (2).

Calculate the lower limit value of *u* using Equation (2).

Substitute 4 for *t* in Equation (2).

Calculate the upper limit value of *u* using Equation (2).

Substitute 2 for *t* in Equation (2).

Apply lower and upper limits for *u* in Equation (1).

Substitute *u* for *du* for *dt* in Equation (1).

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P-1RECh-5 P-2RECh-5 P-3RECh-5 P-4RECh-5 P-5RECh-5 P-6RECh-5 P-7RECh-5 P-8RECh-5 P-9RECh-5 P-10RECh-5 P-11RECh-5 P-12RECh-5 P-13RECh-5 P-14RECh-5 P-15RECh-5 P-16RECh-5 P-17RECh-5 P-18RECh-5 P-19RECh-5 P-20RECh-5 P-21RECh-5 P-22RECh-5 P-23RECh-5 P-24RECh-5 P-25RECh-5 P-26RECh-5 P-27RECh-5 P-28RECh-5 P-29RECh-5 P-30RECh-5 P-31RECh-5 P-32RECh-5 P-33RECh-5 P-34RECh-5 P-35RECh-5 P-36RECh-5 P-37RECh-5 P-38RECh-5 P-39RECh-5 P-40RECh-5 P-41RECh-5 P-42RECh-5 P-43RECh-5 P-44RECh-5 P-45RECh-5 P-46RECh-5 P-47RECh-5 P-48RECh-5 P-49RECh-5 P-50RECh-5 P-51RECh-5 P-52RECh-5 P-53RECh-5 P-54RECh-5 P-55RECh-5 P-56RECh-5 P-57RECh-5 P-58RECh-5 P-59RECh-5 P-60RECh-5 P-61RECh-5 P-62RECh-5 P-63RECh-5 P-66RECh-5 P-69RECh-5 P-70RECh-5 P-71RECh-5 P-72RECh-5 P-1PCh-5 P-2PCh-5 P-3PCh-5 P-5PCh-5 P-6PCh-5 P-7PCh-5 P-8PCh-5 P-9PCh-5 P-10PCh-5 P-11PCh-5 P-14PCh-5 P-15PCh-5 P-18PCh-5 P-19P

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