/*! 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} Q. 7. Why do we require that 0鈮の�-伪... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q. 7. (page 755)

Why do we require that 0鈮�尾-伪鈮�2蟺in the statement

of Theorem 9.13?

Short Answer

Expert verified

According to the definition, to integrate the area 尾>伪

The area should be calculated only once for a given curve.

Step by step solution

01

Given information

Consider the following theorem statement:

Let 伪,尾is any real numbers, such that 0鈮�尾-伪鈮�2蟺路R

R is the polar plane region enclosed by the rays胃=伪and胃=尾

02

Explain why β-α<2π that we don't compute the portion of the area twice.

According to the given information,

A continuous function r=f(胃)then the area of the region Ris 12鈭�伪尾(f(胃))2d胃

To integrate the area 尾>伪according to the description

For each curve, the area should only be calculated once.

That is why 尾-伪<2蟺

So that we don't compute the portion of the area twice.

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

Prove that for an ellipse or a hyperbola the eccentricity is given by

e=the distance between the focithe distance between the vertices

Each of the integrals or integral expressions in Exercises 38-44represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

foci(卤1,0),major axis4

Consider the hyperbola with equation x2A2-y2B2=1.Let F be the focus with coordinates (A2+B2,0).Let e=A2+B2A and l be the vertical line with equation x=Ae. Show that for any point P on the hyperbola, FPDP=e,where D is the point on l closest to P.

In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral

the spiralr=e胃for0鈮�胃鈮�2蟺
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

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.