   Chapter 13.8, Problem 23E ### 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

# In Problems 23-30, round all calculations to 2 decimal places.Total income Suppose that the production from an assembly line can be considered as a continuous income stream with annual rate of flow given by f ( t ) = 100 e 0.1 t t + 1 (in thousands of dollars per year).Use Simpsons Rule with n = 4 to approximate the total income over the first 2 years, given byTotal income = ∫ 0 2 100 e 0.1 t t + 1 d t

To determine

To calculate: The total income over the 2 years with the Simpson’s Rule with n=4 given by 02100e0.1tt+1dt, If suppose the production from the assembly line can be considered as a continuous income stream with annual rate of flow as given above.

Explanation

Given Information:

The provided expression is 02100e0.1tt+1dt.

Formula Used:

As per the Simpson’s Rule:

If f(x) is continuous on [a,b] and [a,b] is divided into an even number n of equal subdivisions, then,

abf(x)dxh3[f(x0)+4f(x1)+2f(x2)+4f(x3)...+2f(xn2)+4f(xn1)+f(xn)]

Where h=ban.

Calculation:

The provided expression,

02100e0.1tt+1dt

In order to apply the rule, the value of h is as follows:

h=204=24=12

Hence, the value of h is 12.

The intervals obtained will be in the addition of h and with n=4:

Substitute, the values of the intervals in the equation:

02100e0

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