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CalculusCalculus10th Edition

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Chapter 10.5, Problem 40E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Finding the Area of a Polar Region Between Two CurvesIn Exercises 37-44, use a graphing utility to graph the polar equations. Find the area of the given region analytically.

Common interior of r = 2 cos θ and r = 2 sin θ

To determine

To calculate: The value of the area of the common interior region of

r=2cosθ and r=2sinθ and to graph the function by the use of graphing calculator.

Explanation

Given:

The two polar equations are r=2cosθ and r=2sinθ.

Formula used:

The area of the polar equation is given by;

A=12∫αβ[f(θ)]2dθ

Where, α and β are limits of the integration.

Calculation:

Consider the polar equations r=2cosθ and r=2sinθ.

Now, draw it on TI-83 calculator. Use the following steps on TI-83 calculator:

Step 1: Press ON to open the calculator.

Step 2: Press MODE button and then scroll down to press pol and press ENTER button.

Step 3: Now, press the button Y= and enter the provided equation.

Step 4: Press WINDOW and then set the window Xmin=−2,Xmax=4,Ymin=−2 and Ymax=3

Step 5: Press ENTER to get the graph.

The graph is shown below and the shaded region is the common interior of polar equation.

Consider the polar equations are: r=2cosθ and r=2sinθ.

Solve the equations simultaneously and get;

2sinθ=2cosθtanθ=1

This gives;

θ=π4,5π4

To get the area between the curves, twice the area obtained by the integration of the polar

equation r=2cosθ from θ=π4 to θ=π2

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Single Variable Calculus: Early Transcendentals

Logarithmic Spiral The curve represented by the equation r=aeb, where a and b are constants, is called a logari...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding the Arc Length of a Polar Curve In Exercises 59-64, use a graphing utility to graph the polar equation ...

Calculus of a Single Variable

Fill in the blanks. The set of all elements in U that are not in A is called the of A.

Finite Mathematics for the Managerial, Life, and Social Sciences

Find the perimeter of a segment of a circle whose boundaries are a chord measuring 24 mm millimetres and an arc...

Elementary Geometry for College Students

What is the partial fraction form of ?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

In Exercises 918, Using the Fundamental Theorem of Line Integrals In Exercises 9-18, evaluate CFdr using the Fu...

Multivariable Calculus

The scalar projection of on is:

Study Guide for Stewart's Multivariable Calculus, 8th

Given are data for two variables, x and y. xi 6 11 15 18 20 yi 6 8 12 20 30 a. Develop an estimated regression ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe the major elements of the APA ethical guidelines concerning human participants in research, including ...

Research Methods for the Behavioral Sciences (MindTap Course List)

A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoki...

Statistics for Business & Economics, Revised (MindTap Course List)

Use a calculator to help solve each problem. Drug absorption in nonsmokers For a nonsmoker, the biological half...

College Algebra (MindTap Course List)

Given the workpieceor tool diameters and the revolutions per minute, determine the cutting speeds in the follow...

Mathematics For Machine Technology

An experiment to assess the effect of predators on ecosystem characteristics such as soil temperature and soil ...

Introduction To Statistics And Data Analysis

Compare and contrast the four scales of measurement (nominal, ordinal, interval, and ratio) and identify exampl...

Research Methods for the Behavioral Sciences (MindTap Course List)

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