(a)
To calculate: The average value of
(a)
Answer to Problem 73E
The average value of
Explanation of Solution
Given information: The given equation of the cardioid is
Formula used: The formula for the average value of the polar coordinate
Calculation:
It is known that the cosine function is a continuous function.
The cardioid
Apply the average value formula of the polar coordinate over the curve
Further simplify.
Therefore, the average value of
(b)
To calculate: The average value of
(b)
Answer to Problem 73E
The average value of
Explanation of Solution
Given information: The given equation of the circle is
Formula used: The formula for the average value of the polar coordinate
Calculation:
In the equation of circle
For a circle
Apply the average value formula of the polar coordinate over the curve
Further simplify.
Therefore, the average value of
(c)
To calculate: The average value of
(c)
Answer to Problem 73E
The average value of
Explanation of Solution
Given information: The given equation of the circle is
Formula used: The formula for the average value of the polar coordinate
Calculation:
Consider the equation
Apply the average value formula of the polar coordinate over the curve
Further simplify.
Therefore, the average value of
Chapter 10 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning