Engineering Board Exam Reviewer · Applications: Area Between Curves · hard
Find the area of the region that lies inside the circle r=3 and outside the cardioid r=1+ .
- 3 π/2 4.71
- π/2 1.57
- 2 π 6.28
- π 3.14
Answer
D. π 3.14
Solution
The curves meet where 3 =1+ , i.e. = π3. By symmetry, A=2· 12 0π/3≤ft[9 2 -(1+ )2 ]d = 0π/3(3+4 2 -2 ),d =≤ft[3 +2 2 -2 ]0π/3=π.
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