Concept explainers
To graph: The polar curves. Also, find the area that lies inside the circle and outside the cardioid.
Answer to Problem 58E
The required area that lies inside the circle and outside the cardioid is
Explanation of Solution
Given information:
The polar curves:
Calculation:
The given curves are
It is known that in a polar
The graph of the given curves is shown below:
It is seen that the shaded region between the curves lie within the interval
Write the area of the given region as:
Simplify the above expression further.
Again, simplify the above expression further.
Hence, the required area that lies inside the circle and outside the cardioid is
Chapter 11 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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