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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Surveying In Exercises 31 and 32, use the Trapezoidal Rule to estimate the number of square feet of land in the lot, where x and y are measured in feet, as shown in the figure. The land is bounded by a stream and two straight roads. (The number of subintervals is shown in the figure.)

Chapter 6.3, Problem 31E, Surveying In Exercises 31 and 32, use the Trapezoidal Rule to estimate the number of square feet of

x 0 100 200 300 400 500
y 125 125 120 112 90 90
x 600 700 800 900 1000
y 95 88 75 35 0

Spreadsheet at LarsonAppliedCalculus.com

To determine

To calculate: The number of square feet of land in the lot where the value of x and y get measured in feet with the use of Trapezoidal Rule according to the provided figure.

The provided figure of graph with subintervals is,

Calculus: An Applied Approach (MindTap Course List), Chapter 6.3, Problem 31E

And Provided table is,

x01002003004005006007008009001000y1251251201129090958875350

Explanation

Given Information:

The provided figure of graph with subintervals is,

And Provided table is,

x01002003004005006007008009001000y1251251201129090958875350

Formula used:

Trapezoidal Rule:

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

abf(x)dx(ba2n)[f(x0)+2f(x1)+...+2f(xn1)+f(xn)]

Calculation:

According to provided figure the graph is divided into 10 sections, so the value of n=10.

The minimum limit of x is 0 and maximum limit of x is 1000, so the value of a=0 and b=1000.

And y=f(x).

Calculation by Trapezoidal Rule:

for that get the end points of subintervals are,

f(x0)=125,f(x1)=125,f(x2)=120,f(x3)=112,f(x4)=90,f(x5

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