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Mathematical Applications for the ...

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

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BuyFindarrow_forward

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 by

Total 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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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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