   Chapter 8.6, Problem 43E

Chapter
Section
Textbook Problem

Work To determine the size of the motor required to operate a press, a company must know the amount of work done when the press moves an object linearly 5 feet. The variable force to move the object is F ( x ) = 100 x 125 − x 3 where F is given in pounds and x gives the position of the unit in feet. Use Simpson’s Rule with n = 12 to approximate the work W (in foot-pounds) done through one cycle when W = ∫ 0 5 F ( x )   d x .

To determine

To calculate: The amount of work done of function F(x)=100x125x2 to with n=12.

Explanation

Given:

The variable force is given by the following function,

F(x)=100x125x2

Where F is given in pounds and x gives the position of the unit in feet.

Formula Used:

For function f, continuous on [a,b] let n be an even integer. Simpsons rule for approximating,

abf(x)dx

And,

abf(x)dxba3n[f(x0)+4f(x1)+2f(x1)+...+2f(xn2)+4f(xn1)+f(xn)]

Calculation:

According to the Simpson’s rule, the work can be calculated as follows, here a=0,b=5 and n=12, it is found that,

Work(50)3(12)[100(0)125(0)3+400(512)125

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