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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the area enclosed by the curve r2 = 9 cos 5θ.

To determine

To find: The area enclosed within in the curve r2=9cos5θ.

Explanation

Given:

The polar equation of the curve with variable r is as follows. ,

r2=9cos5θ

r=±9cos5θ (1)

Assume θ=0°.

Calculate the value of r.

Substitute 0° for θ.in equation (1)

r=13sin(0×π180)r=1

Calculate the value of x.

x=rcosθ

Substitute 1 for r and 0° for θ.

x=rcosθ=1×cos(0×π180)=1

Calculate the value of y.

y=rsinθ

Substitute 0 for r and 0° for θ.

y=1×sin(0×π180)=0

Similarly calculate the values of x and y and the negative values of x and y as x’ and y’ as the values of θ from 0° to 360° as shown in the table (1).

Tabulate the values of x and y in table (1).

theta radius x y x' y'
0.00 3.00 3.00 0.00 -3.00 0.00
10.00 2.41 2.37 0.42 -2.37 -0.42
20.00
30.00
40.00
50.00
60.00 2.12 1.06 1.84 -1.06 -1.84
70.00 2.98 1.02 2.80 -1.02 -2.80
80.00 2.63 0.46 2.59 -0.46 -2.59
90.00 0.00 0.00 0.00 0.00 0.00
100.00
110.00
120.00
130.00 1.75 -1.13 1.34 1.13 -1.34
140.00 2.91 -2.23 1.87 2.23 -1.87
150.00 2.79 -2.42 1.40 2.42 -1.40
160.00 1.25 -1.17 0.43 1.17 -0.43
170.00
180.00
190

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Sect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.1 P-50ESect-10.1 P-51ESect-10.1 P-52ESect-10.2 P-1ESect-10.2 P-2ESect-10.2 P-3ESect-10.2 P-4ESect-10.2 P-5ESect-10.2 P-6ESect-10.2 P-7ESect-10.2 P-8ESect-10.2 P-9ESect-10.2 P-10ESect-10.2 P-11ESect-10.2 P-12ESect-10.2 P-13ESect-10.2 P-14ESect-10.2 P-15ESect-10.2 P-16ESect-10.2 P-17ESect-10.2 P-18ESect-10.2 P-19ESect-10.2 P-20ESect-10.2 P-21ESect-10.2 P-22ESect-10.2 P-23ESect-10.2 P-24ESect-10.2 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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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