Explanation Given information: The region that is inside the circle r = sin θ and outside the cardioid r = 1 − cos θ . Formula used: The area of the polar region enclosed by f ( θ ) for a ≤ θ ≤ b is given by A = 1 2 ∫ a b [ f ( θ ) ] 2 d θ . Calculation: r = sin θ and r = 1 − cos θ .(Given) To find the point of intersection of r = sin θ and r = a ( 1 − cos θ ) , sin θ = ( 1 − cos θ ) . sin θ = ( 1 − cos θ ) s i n θ + cos θ = 1 θ = π 2 The area of the region that is inside the circle r = sin θ and outside the cardioid r = 1 − cos θ is given by A = [ ( A r e a o f r = sin θ ) − ( A r e a o f r = ( 1 − c o s θ ) ) ] A = ( 1 2 ∫ 0 π 2 ( sin θ ) 2 d θ − 1 2 ∫ 0 π 2 ( ( 1 − c o s θ ) ) 2 d θ ) = 1 2 ( ∫ 0 π 2 sin 2 θ d θ − ∫ 0 π 2 ( 1 − c o s θ ) 2 d θ ) = 1 2 ( ∫ 0 π 2 sin 2 θ d θ − ∫ 0 π 2 ( c o

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

See similar textbooks

Videos

Question

Chapter 6.3, Problem 46PS

To determine

To find:The area of the region that is inside the circle r=sinθ and outside the cardioid r=1−cosθ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.3, Problem 45PS

Chapter 6.3, Problem 47PS

Students have asked these similar questions

This question is a previous exam question. I am using it for practice but am stuck

in Q. A firm price of 501: If the Total cast is given by perfect competition sells its products at the TTC = 3Q² +2Q+5. level of output will will be the level of profit at What What Devive the Consumer Curve approach. demand the function maximize this firm's, that using putput level. the indifference prpfit. Q₂. The Total Cost equation in the production of bacon has hypothetical factor a 2 A C= "TC 1000+ 159" +03 ; Where ç. Kash, Bacao - metric bone Compute and 11" tonnes the and average cost at output level of 10. Stretch theme marginal cost of the the shope Carve an the production average, Cost arve 12 tonnes and explain, the relationship between Marginal Cost product es tamen op d Galaxy A71 01 Curve in

if w(x, y, z) = sin' ( xyz) (y zî + x z j + xy k) Find grad (div) at (0.5, 1, 0.5) (xyz)2

Chapter 6 Solutions

Calculus

Ch. 6.1 - Prob. 1PS Ch. 6.1 - Prob. 2PS Ch. 6.1 - Prob. 3PS Ch. 6.1 - Prob. 4PS Ch. 6.1 - Prob. 5PS Ch. 6.1 - Prob. 6PS Ch. 6.1 - Prob. 7PS Ch. 6.1 - Prob. 8PS Ch. 6.1 - Prob. 9PS Ch. 6.1 - Prob. 10PS

Ch. 6.1 - Prob. 11PS Ch. 6.1 - Prob. 12PS Ch. 6.1 - Prob. 13PS Ch. 6.1 - Prob. 14PS Ch. 6.1 - Prob. 15PS Ch. 6.1 - Prob. 16PS Ch. 6.1 - Prob. 17PS Ch. 6.1 - Prob. 18PS Ch. 6.1 - Prob. 19PS Ch. 6.1 - Prob. 20PS Ch. 6.1 - Prob. 21PS Ch. 6.1 - Prob. 22PS Ch. 6.1 - Prob. 23PS Ch. 6.1 - Prob. 24PS Ch. 6.1 - Prob. 25PS Ch. 6.1 - Prob. 26PS Ch. 6.1 - Prob. 27PS Ch. 6.1 - Prob. 28PS Ch. 6.1 - Prob. 29PS Ch. 6.1 - Prob. 30PS Ch. 6.1 - Prob. 31PS Ch. 6.1 - Prob. 32PS Ch. 6.1 - Prob. 33PS Ch. 6.1 - Prob. 34PS Ch. 6.1 - Prob. 35PS Ch. 6.1 - Prob. 36PS Ch. 6.1 - Prob. 37PS Ch. 6.1 - Prob. 38PS Ch. 6.1 - Prob. 39PS Ch. 6.1 - Prob. 40PS Ch. 6.1 - Prob. 41PS Ch. 6.1 - Prob. 42PS Ch. 6.1 - Prob. 43PS Ch. 6.1 - Prob. 44PS Ch. 6.1 - Prob. 45PS Ch. 6.1 - Prob. 46PS Ch. 6.1 - Prob. 47PS Ch. 6.1 - Prob. 48PS Ch. 6.1 - Prob. 49PS Ch. 6.1 - Prob. 50PS Ch. 6.1 - Prob. 51PS Ch. 6.1 - Prob. 52PS Ch. 6.1 - Prob. 53PS Ch. 6.1 - Prob. 54PS Ch. 6.1 - Prob. 55PS Ch. 6.1 - Prob. 56PS Ch. 6.1 - Prob. 57PS Ch. 6.1 - Prob. 58PS Ch. 6.1 - Prob. 59PS Ch. 6.1 - Prob. 60PS Ch. 6.2 - Prob. 1PS Ch. 6.2 - Prob. 2PS Ch. 6.2 - Prob. 3PS Ch. 6.2 - Prob. 4PS Ch. 6.2 - Prob. 5PS Ch. 6.2 - Prob. 6PS Ch. 6.2 - Prob. 7PS Ch. 6.2 - Prob. 8PS Ch. 6.2 - Prob. 9PS Ch. 6.2 - Prob. 10PS Ch. 6.2 - Prob. 11PS Ch. 6.2 - Prob. 12PS Ch. 6.2 - Prob. 13PS Ch. 6.2 - Prob. 14PS Ch. 6.2 - Prob. 15PS Ch. 6.2 - Prob. 16PS Ch. 6.2 - Prob. 17PS Ch. 6.2 - Prob. 18PS Ch. 6.2 - Prob. 19PS Ch. 6.2 - Prob. 20PS Ch. 6.2 - Prob. 21PS Ch. 6.2 - Prob. 22PS Ch. 6.2 - Prob. 23PS Ch. 6.2 - Prob. 24PS Ch. 6.2 - Prob. 25PS Ch. 6.2 - Prob. 26PS Ch. 6.2 - Prob. 27PS Ch. 6.2 - Prob. 28PS Ch. 6.2 - Prob. 29PS Ch. 6.2 - Prob. 30PS Ch. 6.2 - Prob. 31PS Ch. 6.2 - Prob. 32PS Ch. 6.2 - Prob. 33PS Ch. 6.2 - Prob. 34PS Ch. 6.2 - Prob. 35PS Ch. 6.2 - Prob. 36PS Ch. 6.2 - Prob. 37PS Ch. 6.2 - Prob. 38PS Ch. 6.2 - Prob. 39PS Ch. 6.2 - Prob. 40PS Ch. 6.2 - Prob. 41PS Ch. 6.2 - Prob. 42PS Ch. 6.2 - Prob. 43PS Ch. 6.2 - Prob. 44PS Ch. 6.2 - Prob. 45PS Ch. 6.2 - Prob. 46PS Ch. 6.2 - Prob. 47PS Ch. 6.2 - Prob. 48PS Ch. 6.2 - Prob. 49PS Ch. 6.2 - Prob. 50PS Ch. 6.2 - Prob. 51PS Ch. 6.2 - Prob. 52PS Ch. 6.2 - Prob. 53PS Ch. 6.2 - Prob. 54PS Ch. 6.2 - Prob. 55PS Ch. 6.2 - Prob. 56PS Ch. 6.2 - Prob. 57PS Ch. 6.2 - Prob. 58PS Ch. 6.2 - Prob. 59PS Ch. 6.2 - Prob. 60PS Ch. 6.3 - Prob. 1PS Ch. 6.3 - Prob. 2PS Ch. 6.3 - Prob. 3PS Ch. 6.3 - Prob. 4PS Ch. 6.3 - Prob. 5PS Ch. 6.3 - Prob. 6PS Ch. 6.3 - Prob. 7PS Ch. 6.3 - Prob. 8PS Ch. 6.3 - Prob. 9PS Ch. 6.3 - Prob. 10PS Ch. 6.3 - Prob. 11PS Ch. 6.3 - Prob. 12PS Ch. 6.3 - Prob. 13PS Ch. 6.3 - Prob. 14PS Ch. 6.3 - Prob. 15PS Ch. 6.3 - Prob. 16PS Ch. 6.3 - Prob. 17PS Ch. 6.3 - Prob. 18PS Ch. 6.3 - Prob. 19PS Ch. 6.3 - Prob. 20PS Ch. 6.3 - Prob. 21PS Ch. 6.3 - Prob. 22PS Ch. 6.3 - Prob. 23PS Ch. 6.3 - Prob. 24PS Ch. 6.3 - Prob. 25PS Ch. 6.3 - Prob. 26PS Ch. 6.3 - Prob. 27PS Ch. 6.3 - Prob. 28PS Ch. 6.3 - Prob. 29PS Ch. 6.3 - Prob. 30PS Ch. 6.3 - Prob. 31PS Ch. 6.3 - Prob. 32PS Ch. 6.3 - Prob. 33PS Ch. 6.3 - Prob. 34PS Ch. 6.3 - Prob. 35PS Ch. 6.3 - Prob. 36PS Ch. 6.3 - Prob. 37PS Ch. 6.3 - Prob. 38PS Ch. 6.3 - Prob. 39PS Ch. 6.3 - Prob. 40PS Ch. 6.3 - Prob. 41PS Ch. 6.3 - Prob. 42PS Ch. 6.3 - Prob. 43PS Ch. 6.3 - Prob. 44PS Ch. 6.3 - Prob. 45PS Ch. 6.3 - Prob. 46PS Ch. 6.3 - Prob. 47PS Ch. 6.3 - Prob. 48PS Ch. 6.3 - Prob. 49PS Ch. 6.3 - Prob. 50PS Ch. 6.3 - Prob. 51PS Ch. 6.3 - Prob. 52PS Ch. 6.3 - Prob. 53PS Ch. 6.3 - Prob. 54PS Ch. 6.3 - Prob. 55PS Ch. 6.3 - Prob. 56PS Ch. 6.3 - Prob. 57PS Ch. 6.3 - Prob. 58PS Ch. 6.3 - Prob. 59PS Ch. 6.3 - Prob. 60PS Ch. 6.4 - Prob. 1PS Ch. 6.4 - Prob. 2PS Ch. 6.4 - Prob. 3PS Ch. 6.4 - Prob. 4PS Ch. 6.4 - Prob. 5PS Ch. 6.4 - Prob. 6PS Ch. 6.4 - Prob. 7PS Ch. 6.4 - Prob. 8PS Ch. 6.4 - Prob. 9PS Ch. 6.4 - Prob. 10PS Ch. 6.4 - Prob. 11PS Ch. 6.4 - Prob. 12PS Ch. 6.4 - Prob. 13PS Ch. 6.4 - Prob. 14PS Ch. 6.4 - Prob. 15PS Ch. 6.4 - Prob. 16PS Ch. 6.4 - Prob. 17PS Ch. 6.4 - Prob. 18PS Ch. 6.4 - Prob. 19PS Ch. 6.4 - Prob. 20PS Ch. 6.4 - Prob. 21PS Ch. 6.4 - Prob. 22PS Ch. 6.4 - Prob. 23PS Ch. 6.4 - Prob. 24PS Ch. 6.4 - Prob. 25PS Ch. 6.4 - Prob. 26PS Ch. 6.4 - Prob. 27PS Ch. 6.4 - Prob. 28PS Ch. 6.4 - Prob. 29PS Ch. 6.4 - Prob. 30PS Ch. 6.4 - Prob. 31PS Ch. 6.4 - Prob. 32PS Ch. 6.4 - Prob. 33PS Ch. 6.4 - Prob. 34PS Ch. 6.4 - Prob. 35PS Ch. 6.4 - Prob. 36PS Ch. 6.4 - Prob. 37PS Ch. 6.4 - Prob. 38PS Ch. 6.4 - Prob. 39PS Ch. 6.4 - Prob. 40PS Ch. 6.4 - Prob. 41PS Ch. 6.4 - Prob. 42PS Ch. 6.4 - Prob. 43PS Ch. 6.4 - Prob. 44PS Ch. 6.4 - Prob. 45PS Ch. 6.4 - Prob. 46PS Ch. 6.4 - Prob. 47PS Ch. 6.4 - Prob. 48PS Ch. 6.4 - Prob. 49PS Ch. 6.4 - Prob. 50PS Ch. 6.4 - Prob. 51PS Ch. 6.4 - Prob. 52PS Ch. 6.4 - Prob. 53PS Ch. 6.4 - Prob. 54PS Ch. 6.4 - Prob. 55PS Ch. 6.4 - Prob. 56PS Ch. 6.4 - Prob. 57PS Ch. 6.4 - Prob. 58PS Ch. 6.4 - Prob. 59PS Ch. 6.4 - Prob. 60PS Ch. 6.5 - Prob. 1PS Ch. 6.5 - Prob. 2PS Ch. 6.5 - Prob. 3PS Ch. 6.5 - Prob. 4PS Ch. 6.5 - Prob. 5PS Ch. 6.5 - Prob. 6PS Ch. 6.5 - Prob. 7PS Ch. 6.5 - Prob. 8PS Ch. 6.5 - Prob. 9PS Ch. 6.5 - Prob. 10PS Ch. 6.5 - Prob. 11PS Ch. 6.5 - Prob. 12PS Ch. 6.5 - Prob. 13PS Ch. 6.5 - Prob. 14PS Ch. 6.5 - Prob. 15PS Ch. 6.5 - Prob. 16PS Ch. 6.5 - Prob. 17PS Ch. 6.5 - Prob. 18PS Ch. 6.5 - Prob. 19PS Ch. 6.5 - Prob. 20PS Ch. 6.5 - Prob. 21PS Ch. 6.5 - Prob. 22PS Ch. 6.5 - Prob. 23PS Ch. 6.5 - Prob. 24PS Ch. 6.5 - Prob. 25PS Ch. 6.5 - Prob. 26PS Ch. 6.5 - Prob. 27PS Ch. 6.5 - Prob. 28PS Ch. 6.5 - Prob. 29PS Ch. 6.5 - Prob. 30PS Ch. 6.5 - Prob. 31PS Ch. 6.5 - Prob. 32PS Ch. 6.5 - Prob. 33PS Ch. 6.5 - Prob. 34PS Ch. 6.5 - Prob. 35PS Ch. 6.5 - Prob. 36PS Ch. 6.5 - Prob. 37PS Ch. 6.5 - Prob. 38PS Ch. 6.5 - Prob. 39PS Ch. 6.5 - Prob. 40PS Ch. 6.5 - Prob. 41PS Ch. 6.5 - Prob. 42PS Ch. 6.5 - Prob. 43PS Ch. 6.5 - Prob. 44PS Ch. 6.5 - Prob. 45PS Ch. 6.5 - Prob. 46PS Ch. 6.5 - Prob. 47PS Ch. 6.5 - Prob. 48PS Ch. 6.5 - Prob. 49PS Ch. 6.5 - Prob. 50PS Ch. 6.5 - Prob. 51PS Ch. 6.5 - Prob. 52PS Ch. 6.5 - Prob. 53PS Ch. 6.5 - Prob. 54PS Ch. 6.5 - Prob. 55PS Ch. 6.5 - Prob. 56PS Ch. 6.5 - Prob. 57PS Ch. 6.5 - Prob. 58PS Ch. 6.5 - Prob. 59PS Ch. 6.5 - Prob. 60PS Ch. 6.6 - Prob. 1PS Ch. 6.6 - Prob. 2PS Ch. 6.6 - Prob. 3PS Ch. 6.6 - Prob. 4PS Ch. 6.6 - Prob. 5PS Ch. 6.6 - Prob. 6PS Ch. 6.6 - Prob. 7PS Ch. 6.6 - Prob. 8PS Ch. 6.6 - Prob. 9PS Ch. 6.6 - Prob. 10PS Ch. 6.6 - Prob. 11PS Ch. 6.6 - Prob. 12PS Ch. 6.6 - Prob. 13PS Ch. 6.6 - Prob. 14PS Ch. 6.6 - Prob. 15PS Ch. 6.6 - Prob. 16PS Ch. 6.6 - Prob. 17PS Ch. 6.6 - Prob. 18PS Ch. 6.6 - Prob. 19PS Ch. 6.6 - Prob. 20PS Ch. 6.6 - Prob. 21PS Ch. 6.6 - Prob. 22PS Ch. 6.6 - Prob. 23PS Ch. 6.6 - Prob. 24PS Ch. 6.6 - Prob. 25PS Ch. 6.6 - Prob. 26PS Ch. 6.6 - Prob. 27PS Ch. 6.6 - Prob. 28PS Ch. 6.6 - Prob. 29PS Ch. 6.6 - Prob. 30PS Ch. 6.6 - Prob. 31PS Ch. 6.6 - Prob. 32PS Ch. 6.6 - Prob. 33PS Ch. 6.6 - Prob. 34PS Ch. 6.6 - Prob. 35PS Ch. 6.6 - Prob. 36PS Ch. 6.6 - Prob. 37PS Ch. 6.6 - Prob. 38PS Ch. 6.6 - Prob. 39PS Ch. 6.6 - Prob. 40PS Ch. 6.6 - Prob. 41PS Ch. 6.6 - Prob. 42PS Ch. 6.6 - Prob. 43PS Ch. 6.6 - Prob. 44PS Ch. 6.6 - Prob. 45PS Ch. 6.6 - Prob. 46PS Ch. 6.6 - Prob. 47PS Ch. 6.6 - Prob. 48PS Ch. 6.6 - Prob. 49PS Ch. 6.6 - Prob. 50PS Ch. 6.6 - Prob. 51PS Ch. 6.6 - Prob. 52PS Ch. 6.6 - Prob. 53PS Ch. 6.6 - Prob. 54PS Ch. 6.6 - Prob. 55PS Ch. 6.6 - Prob. 56PS Ch. 6.6 - Prob. 57PS Ch. 6.6 - Prob. 58PS Ch. 6.6 - Prob. 59PS Ch. 6.6 - Prob. 60PS Ch. 6 - Prob. 1PE Ch. 6 - Prob. 2PE Ch. 6 - Prob. 3PE Ch. 6 - Prob. 4PE Ch. 6 - Prob. 5PE Ch. 6 - Prob. 6PE Ch. 6 - Prob. 7PE Ch. 6 - Prob. 8PE Ch. 6 - Prob. 9PE Ch. 6 - Prob. 10PE Ch. 6 - Prob. 11PE Ch. 6 - Prob. 12PE Ch. 6 - Prob. 13PE Ch. 6 - Prob. 14PE Ch. 6 - Prob. 15PE Ch. 6 - Prob. 16PE Ch. 6 - Prob. 17PE Ch. 6 - Prob. 18PE Ch. 6 - Prob. 19PE Ch. 6 - Prob. 20PE Ch. 6 - Prob. 21PE Ch. 6 - Prob. 22PE Ch. 6 - Prob. 23PE Ch. 6 - Prob. 24PE Ch. 6 - Prob. 25PE Ch. 6 - Prob. 26PE Ch. 6 - Prob. 27PE Ch. 6 - Prob. 28PE Ch. 6 - Prob. 29PE Ch. 6 - Prob. 30PE Ch. 6 - Prob. 1SP Ch. 6 - Prob. 2SP Ch. 6 - Prob. 3SP Ch. 6 - Prob. 4SP Ch. 6 - Prob. 5SP Ch. 6 - Prob. 6SP Ch. 6 - Prob. 7SP Ch. 6 - Prob. 8SP Ch. 6 - Prob. 9SP Ch. 6 - Prob. 10SP Ch. 6 - Prob. 11SP Ch. 6 - Prob. 12SP Ch. 6 - Prob. 13SP Ch. 6 - Prob. 14SP Ch. 6 - Prob. 15SP Ch. 6 - Prob. 16SP Ch. 6 - Prob. 17SP Ch. 6 - Prob. 18SP Ch. 6 - Prob. 19SP Ch. 6 - Prob. 20SP Ch. 6 - Prob. 21SP Ch. 6 - Prob. 22SP Ch. 6 - Prob. 23SP Ch. 6 - Prob. 24SP Ch. 6 - Prob. 25SP Ch. 6 - Prob. 26SP Ch. 6 - Prob. 27SP Ch. 6 - Prob. 28SP Ch. 6 - Prob. 29SP Ch. 6 - Prob. 30SP Ch. 6 - Prob. 31SP Ch. 6 - Prob. 32SP Ch. 6 - Prob. 33SP Ch. 6 - Prob. 34SP Ch. 6 - Prob. 35SP Ch. 6 - Prob. 36SP Ch. 6 - Prob. 37SP Ch. 6 - Prob. 38SP Ch. 6 - Prob. 39SP Ch. 6 - Prob. 40SP Ch. 6 - Prob. 41SP Ch. 6 - Prob. 42SP Ch. 6 - Prob. 43SP Ch. 6 - Prob. 44SP Ch. 6 - Prob. 45SP Ch. 6 - Prob. 46SP Ch. 6 - Prob. 47SP Ch. 6 - Prob. 48SP Ch. 6 - Prob. 49SP Ch. 6 - Prob. 50SP Ch. 6 - Prob. 51SP Ch. 6 - Prob. 52SP Ch. 6 - Prob. 53SP Ch. 6 - Prob. 54SP Ch. 6 - Prob. 55SP Ch. 6 - Prob. 56SP Ch. 6 - Prob. 57SP Ch. 6 - Prob. 58SP Ch. 6 - Prob. 59SP Ch. 6 - Prob. 60SP Ch. 6 - Prob. 61SP Ch. 6 - Prob. 62SP Ch. 6 - Prob. 63SP Ch. 6 - Prob. 64SP Ch. 6 - Prob. 65SP Ch. 6 - Prob. 66SP Ch. 6 - Prob. 67SP Ch. 6 - Prob. 68SP Ch. 6 - Prob. 69SP Ch. 6 - Prob. 70SP Ch. 6 - Prob. 71SP Ch. 6 - Prob. 72SP Ch. 6 - Prob. 73SP Ch. 6 - Prob. 74SP Ch. 6 - Prob. 75SP Ch. 6 - Prob. 76SP Ch. 6 - Prob. 77SP Ch. 6 - Prob. 78SP Ch. 6 - Prob. 79SP Ch. 6 - Prob. 80SP Ch. 6 - Prob. 81SP Ch. 6 - Prob. 82SP Ch. 6 - Prob. 83SP Ch. 6 - Prob. 84SP Ch. 6 - Prob. 85SP Ch. 6 - Prob. 86SP Ch. 6 - Prob. 87SP Ch. 6 - Prob. 88SP Ch. 6 - Prob. 89SP Ch. 6 - Prob. 90SP Ch. 6 - Prob. 91SP Ch. 6 - Prob. 92SP Ch. 6 - Prob. 93SP Ch. 6 - Prob. 94SP Ch. 6 - Prob. 95SP Ch. 6 - Prob. 96SP Ch. 6 - Prob. 97SP Ch. 6 - Prob. 98SP Ch. 6 - Prob. 99SP

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The area of the region that is inside the circle r = sin θ and outside the cardioid r = 1 − cos θ .

Solution Summary: The author calculates the area of the polar region inside the circle r=mathrmsintheta and outside the cardioid

Videos

To find:The area of the region that is inside the circle r=sinθ and outside the cardioid r=1−cosθ .

Want to see the full answer?

Chapter 6 Solutions