Q. 34 in exercise 31-36 find a definit... [FREE SOLUTION]

Chapter 9: Q. 34 (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 entire limacon $r = 1 + 2 \sin 胃$

Short Answer

Expert verified

The integral can be given as $L = {鈭�}_{0}^{2 蟺} \sqrt{(2 \cos 胃) + (1 + 2 \sin 胃)} d 胃$ and arc length can be given as 13.37units

Step by step solution

Given information

The entire limacon $r = 1 + 2 \sin 胃$

Evaluate

We know that length of limacon can be given as

$L = {鈭�}_{0}^{2 蟺} \sqrt{{(r')}^{2} + {(r)}^{2}} d r S u b s t i t u t i n g t h e v a l u e s w e g e t L = {鈭�}_{0}^{2 蟺} \sqrt{{(2 \cos 胃)}^{2} + {(1 + 2 \sin 胃)}^{2}} d r w e f i r s t s i m p l i f y t h e g i v e n e x p r e s s i o n w e g e t, L = {鈭�}_{0}^{2 蟺} \sqrt{4 \cos^{2} 胃 + 1 + 4 \sin^{2} 胃 + 4 \sin 胃} d 胃 L = {鈭�}_{0}^{2 蟺} \sqrt{5 + 4 \sin 胃} d 胃 N o w u \sin g C A S c a l c u l a t o r w e g e t, L = 13.36 u n i t s$

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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 entire limacon $r = 1 + 2 \sin 胃$

Short Answer

Step by step solution

Given information

Evaluate

One App. One Place for Learning.

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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 entire limacon r=1+2sin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

Mechanics Maths

Discrete Mathematics

Statistics

Calculus

Logic and Functions

Geometry

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 entire limacon $r = 1 + 2 \sin 胃$