(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
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