The outer circle in the figure has radius 1 and the centers of the interior circular arcs lie on the outer circle. Find the area of the shaded region.
To find:
The area of the shaded region
Answer to Problem 1P
Solution:
Explanation of Solution
1) Concept:
Draw the figure on
2) Calculation:
Consider the given figure on
Consider the circle with center
So the equation of the circle is
The figure above describes the circular arc from
To write the equation of circle in the form of polar coordinates
Substitute
Use the quadratic formula,
For
To find the total area of shaded region A
The area of green region is
That is,
To evaluate the second integral by using substitution method,
Substitute
Integrate the above equation, by using the following formula:
Conclusion:
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