Q. 31 In exercises 31-36 find a defini... [FREE SOLUTION]

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
$O n e p e t a l o f t h e p o l a r r o s e r = \cos 2 胃$

Short Answer

Expert verified

The integral can be given as ${鈭�}_{0}^{2 蟺} \sqrt{{(1 + \cos 2 胃)}^{2} + {(- \sin 2 胃)}^{2}} d 胃$ 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 $r = \cos 2 胃$

Find the integral and evaluate it using computer algebra system

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

${鈭�}_{0}^{2 蟺} \sqrt{(f {(胃))}^{2} + (f' {(胃))}^{2}} d 胃$

We have

$r = \cos 2 胃 r' = - 2 \sin 2 胃$

Substituting the values we get

${鈭�}_{0}^{2 蟺} \sqrt{{(\cos 2 胃)}^{2} + {(- 2 \sin 2 胃)}^{2}} d 胃$

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

$7.43$ units

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91影视

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
$O n e p e t a l o f t h e p o l a r r o s e r = \cos 2 胃$

Short Answer

Step by step solution

Given information

Find the integral and evaluate it using computer algebra system

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91影视

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=cos2胃

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

Statistics

Geometry

Applied Mathematics

Pure Maths

Decision Maths

Theoretical and Mathematical Physics

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
$O n e p e t a l o f t h e p o l a r r o s e r = \cos 2 胃$