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

0 10 20 30 40 50 60
y 75 81 84 76 67 68 69
X 70 80 90 100 110 120
y 72 68 56 42 23 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 32E

And Provided table is,

x0102030405060708090100110120y7581847667686972685642230

Explanation

Given Information:

The provided figure of graph with subintervals is,

And Provided table is,

x0102030405060708090100110120y7581847667686972685642230

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 12 sections, so the value of n=12.

The minimum limit of x is 0 and maximum limit of x is 120, so the value of a=0 and b=120.

And y=f(x).

Calculation by Trapezoidal Rule:

for that get the end points of subintervals are,

f(x0)=75,f(x1)=81,f(x2)=84,f(x3)=76,f(x4)=67,f(x5)=68,f(x6)=69,f

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