Chapter 9: Q. 31 (page 756)

In exercises 31-36 find a definite integral that represents the length of the specified polar curve, and then use a graphing calculator or computer algebra system to approximate the value of integral
$O n e p e t a l o f t h e p o l a r r o s e r = \cos 2 θ$

Short Answer

Expert verified

The integral can be given as $\int_{0}^{2 π} \sqrt{{(1 + \cos 2 θ)}^{2} + {(- \sin 2 θ)}^{2}} d θ$ and the length of the polar curve is 7.43 units

Step by step solution

Given information

We are given a polar rose of equation $r = \cos 2 θ$

Find the integral and evaluate it using computer algebra system

We know that the length of the polar rose can be given as

$\int_{0}^{2 π} \sqrt{(f {(θ))}^{2} + (f' {(θ))}^{2}} d θ$

We have

$r = \cos 2 θ r' = - 2 \sin 2 θ$

Substituting the values we get

$\int_{0}^{2 π} \sqrt{{(\cos 2 θ)}^{2} + {(- 2 \sin 2 θ)}^{2}} d θ$

We use computer algebra system to evaluate the integral we get,

$7.43$ units

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In exercises 31-36 find a definite integral that represents the length of the specified polar curve, and then use a graphing calculator or computer algebra system to approximate the value of integral
$O n e p e t a l o f t h e p o l a r r o s e r = \cos 2 θ$

Short Answer

Step by step solution

Given information

Find the integral and evaluate it using computer algebra system

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In exercises 31-36 find a definite integral that represents the length of the specified polar curve, and then use a graphing calculator or computer algebra system to approximate the value of integralOnepetalofthepolarroser=cos2θ

Short Answer

Step by step solution

Given information

Find the integral and evaluate it using computer algebra system

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Calculus

Statistics

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In exercises 31-36 find a definite integral that represents the length of the specified polar curve, and then use a graphing calculator or computer algebra system to approximate the value of integral
$O n e p e t a l o f t h e p o l a r r o s e r = \cos 2 θ$