Q. 36 in exercise 31-36 find a definit... [FREE SOLUTION]

Chapter 9: Q. 36 (page 756)

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral
The limacon $r = 2 + \cos 胃$

Short Answer

Expert verified

The integral can be given as ${鈭�}_{0}^{2 蟺} \sqrt{{(- \sin 胃)}^{2} + {(2 + \cos 胃)}^{2}} d 胃$ and length can be given as 13.36 units.

Step by step solution

Given information

We are given a limacon $r = 2 + \cos 胃$

Evaluate

We know that arc length can be given as

$L = {鈭�}_{a}^{b} \sqrt{{(r')}^{2} + {(r)}^{2}} d r S u b s t i t u t i n g t h e v a l u e s w e g e t L = {鈭�}_{0}^{2 蟺} \sqrt{{(- \sin 胃)}^{2} + {(2 + \cos 胃)}^{2}} d 胃 W e f i r s t s i m p l i f y t h e g i v e n e x p r e s s i o n L = {鈭�}_{0}^{2 蟺} \sqrt{\sin^{2} 胃 + 4 + 4 \cos 胃 + \cos^{2} 胃} L = {鈭�}_{0}^{2 蟺} \sqrt{5 + 4 \cos 胃} U \sin g C A S c a l c u l a t o r, W e e v a l u a t e t h e i n t e g r a l L = 13.36 u n i t s$

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91影视

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral
The limacon $r = 2 + \cos 胃$

Short Answer

Step by step solution

Given information

Evaluate

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91影视

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integralThe limaconr=2+cos胃

Short Answer

Step by step solution

Given information

Evaluate

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Statistics

Discrete Mathematics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral
The limacon $r = 2 + \cos 胃$