Chapter 8.6, Problem 43E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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)=100x125âˆ’x2

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,

âˆ«abf(x)dx

And,

âˆ«abf(x)dxâ‰ˆbâˆ’a3n[f(x0)+4f(x1)+2f(x1)+...+2f(xnâˆ’2)+4f(xnâˆ’1)+f(xn)]

Calculation:

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

Workâ‰ˆ(5âˆ’0)3(12)[100(0)125âˆ’(0)3+400(512)125âˆ’

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started