/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q16P Find the arc length of one arch ... [FREE SOLUTION] | 91影视

91影视

Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology
Features
Features

Discover all of these amazing features with a free account.

Flashcards

91影视 AI

Notes

Study Plans

Study Sets
What鈥檚 new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
91影视
Discover

All the hacks around your studies and career - in one place.

Find a degree

Magazine
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

The largest student job board with the most exciting opportunities.

Verified student deals from top brands.

Discover our mobile app to take your studies anywhere.

Learning Materials

Features

Discover

Chapter 11: Q16P (page 559)

Find the arc length of one arch of $y = s i n x$ .

Short Answer

Expert verified

The length of one arc is $\sqrt{2} E (蟺, \frac{1}{\sqrt{2}}) 鈮� 3.82019$ .

Step by step solution

01

Given Information

The function is $y = \sin x$ .

02

Definition of the differential element of displacement.

The differential element of displacement is defined as $鈭� d s = 鈭� \sqrt{{dx}^{2} + {dx}^{2}}$ .

03

Find the value of Integral

The formula of differential element of displacement is $鈭� d s = 鈭� \sqrt{d x^{2} + d y^{2}}$ .

$鈭� d s = 鈭� \sqrt{d x^{2} (1 + \frac{d y^{2}}{d x^{2}})} 鈭� d s = 鈭� \sqrt{(1 + \frac{d y^{2}}{d x^{2}})} d x$

Substitute the value given below in the equation mentioned above.

$y = \sin x \frac{d y}{d x} = \cos x$

The equation becomes as follows:

$鈭� d s = 鈭� \sqrt{(1 + \cos^{2} x)} d x 鈭� d s = 鈭� \sqrt{(1 + (1 - \sin^{2} x))} d x 鈭� d s = 鈭� \sqrt{(2 - \sin^{2} x)} d x 鈭� d s = \sqrt{2} 鈭� \sqrt{(1 - \frac{\sin^{2} x}{2})} d x$

The formula for the elliptical function is $E (\frac{蟺}{2}, K) = {鈭�}_{0}^{\frac{蟺}{2}} \sqrt{1 - k^{2} \sin^{2} 胃} d 胃$ .

The equation becomes as follows:

$鈭� d s = \sqrt{2} 鈭� \sqrt{(1 - \frac{\sin^{2} x}{2})} d x 鈭� d s = \sqrt{2} E (蟺, \frac{1}{\sqrt{2}}) 鈭� d s 鈮� 3.82019$

The length of one arc is $\sqrt{2} E (蟺, \frac{1}{\sqrt{2}}) 鈮� 3.82019$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The following expression occurs in statistical mechanics:

$P = \frac{n!}{(n p + u)! (n q - u)!} p^{n p + u} q^{n q - u} .$

Use Stirling鈥檚 formula to show that

$\frac{1}{P} 鈻� x^{n p x} y^{n q y} \sqrt{2 蟺苍辫辩虫测}, w h e r e x = 1 + \frac{u}{n p}, y = 1 - \frac{u}{n q}, p + q = 1 .$

Hint: Show that ${(n p)}^{n p + u} {(n q)}^{n q - u} = n^{n} p^{n p + u} q^{n q - u}$ .

Computer plot graphs of

(a) E_n(x) for n = 0-10and x = 0.2.

(b) E₁(x) and E_n(x)for x = 0-2.

(c) the sine integral $S_{i} (x) = {鈭�}_{0}^{x} \frac{s i n t}{t} d t$ and the cosine integral $C_{i} (x) = {鈭�}_{0}^{鈭�} \frac{C o s t}{t} d t$ for $x = 0 - 4 蟺$ .

${鈭�}_{0}^{1} \frac{1}{\sqrt{1 - t^{2}} \sqrt{1 - \frac{t^{2}}{4}}} d t$

Sketch or computer plot a graph of the function $y = e^{- x^{2}}$ .

In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.

11. ${鈭�}_{\frac{- 蟺}{2}}^{\frac{3 蟺}{8}} \frac{1}{\sqrt{1 - \frac{9}{10} \sin^{2} 胃}} d 胃$

See all solutions

Recommended explanations on Physics Textbooks

Work Energy and Power

Read Explanation

Wave Optics

Read Explanation

Astrophysics

Read Explanation

Magnetism

Read Explanation

Rotational Dynamics

Read Explanation

Medical Physics

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.