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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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Surface Area Use the Midpoint Rule to estimate the surface area of the pond shown in the figure.

Chapter 5.6, Problem 29E, Surface Area Use the Midpoint Rule to estimate the surface area of the pond shown in the figure.

To determine

To calculate: The surface area of the pond shown in the figure below by application of the midpoint rule,

Calculus: An Applied Approach (MindTap Course List), Chapter 5.6, Problem 29E

Explanation

Given Information:

The figure showing the pond is provided below as,

Formula used:

The midpoint rule states that the midpoint (m) of each interval (a, b) is given by

m=a+b2.

Calculation:

The width of each area is 20 ft.

Calculate the midpoint of each of the intervals provided as,

[0,50],[50,54],[54,82],[82,82],[82,73],[73,75],[75,80],[80,]

Calculate the midpoint of the interval [0,50],

[0,50]=0+502=25

Calculate the midpoint of the interval [50,54],

[50,54]=50+542=52

Calculate the midpoint of the interval [54,82],

[54,82]=54+822=68

Calculate the midpoint of the interval [82,82]

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