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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.6, Problem 31E
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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 oil spill shown in the figure.

Chapter 5.6, Problem 31E, Surface Area Use the Midpoint Rule to estimate the surface area of the oil spill shown in the

To determine

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

Calculus: An Applied Approach (MindTap Course List), Chapter 5.6, Problem 31E

Explanation

Given Information:

The figure showing the oil spill 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 4 mi.

Calculate the midpoint of each interval as,

[0,11],[11,13.5],[13.5,14.2],[14.2,14],[14,14.2],[14.2,15],[15,13.5],[13.5,∞]

The midpoint of the interval [0,11] is,

[0,11]=0+112=5.5

The midpoint of the interval [11,13.5] is,

[11,13.5]=11+13.52=12.25

The midpoint of the interval [13.5,14.2] is,

[13.5,14.2]=13.5+14.22=13.85

The midpoint of the interval [14.2,14] is,

[14

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