   Chapter 13.8, Problem 34E ### 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

# Development costs A land developer is planning to dig a small lake and build a group of homes around it. To estimate the cost of the project, the area of the lake must be calculated from the proposed measurements (in feet) given in Figure 13.35 and in the data in the table. Use Simpson's Rule to approximate the area of the lake. x Width w(x) 0 0 100 300 200 200 300 400 400 0 To determine

To calculate: The area of the lake by the Trapezoidal Rule if the area of the lake is as per the given table and the diagram:

 x Width w(x) 0 0 100 300 200 200 300 400 400 0

The provided graph is shown below: Explanation

Given Information:

The area of the lake is as per the given table and the diagram:

 x Width w(x) 0 0 100 300 200 200 300 400 400 0

The provided graph is shown below:

Formula Used:

As per the Trapezoidal Rule:

If f is continuous on [a,b], then,

abf(x)dxh2[f(x0)+2f(x1)+2f(x2)+2f(x3)++2f(xn2)+2f(xn1)+f(xn)]

Where h=ban and n is the number of equal subdivisions of [a,b].

Calculation:

The area of the lake is as per the given table and the diagram:

 x Width w(x) 0 0 100 300 200 200 300 400 400 0

The provided graph is shown below:

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

h=100

So, the interval [0,400] is divided into 4 subintervals as follows,

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