   Chapter 13.2, Problem 63E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Production In Problems 65 and 66, the rate of production of a new line of products is given by d x d t = 200 [ 1 + 400 ( t + 40 ) 2 ] where x is the number of items produced and t is the number of weeks the products have been in production.How many units were produced in the first 5 weeks?

To determine

To calculate: The number of units produced in first 5 weeks where the rate of production is dxdt=200[1+400(t+40)2] where x is the number of items and t is the number of weeks.

Explanation

Given Information:

The rate of production is dxdt=200[1+400(t+40)2].

Formula used:

To calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

The value of the integral xndx=xn+1n+1.

Calculation:

Consider the rate of production is dxdt=200[1+400(t+40)2].

Since, the number of units produced is the definite integral from 0 to 5.

Thus, number of units produced is the integral x=05200(1+400(t+40)2)dt.

Recall that to calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

Simplify the integral by the use of the formula xndx=xn+1n+1,

05200(1+400(t+40)2)dt=2000<

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