   Chapter 5.5, Problem 86E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

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 d x d t = 5000 ( 1 − 100 ( t + 10 ) 2 )   calculators / week (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:

dxdt=5000[1100(t+10)2]

Calculation:

Show the integral function after applying the limits.

245000[1100(t+10)2]dt (1)

The region lies between t=4 and t=2.

Consider u=t+10 (2)

Differentiate both sides of the Equation (2).

du=dt

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

Substitute 4 for t in Equation (2).

u=4+10=14

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

Substitute 2 for t in Equation (2).

u=2+10=12

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

Substitute u for (t+10) and du for dt in Equation (1).

245000[1100(t+10)2]dt=12145000

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