To find: The area of the common region enclosed by the circle
Answer to Problem 55E
The area of the region enclosed by the given circle and the cardioid is
Explanation of Solution
Given information: Equation of circle is
Formula used: The double-angle formula for cosine function is given by:
Calculation:
Equate the given equation of the circle and the cardioid to find the value of
According to the fact
Draw the graph of the given circle and cardioid.
Figure (1)
From the above graph it can be observed that
Calculate the required area enclosed by the curves.
Further simplify the integral.
Apply the trigonometric identity
Further simplify.
Evaluate the integral
For
Use the above results determine the integral
Therefore, the area of the region enclosed by the given circle and the cardioid is
Chapter 10 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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