Engineering Board Exam Reviewer · Applications: Area Between Curves · hard
Find the area enclosed by the astroid x=2 3t, y=2 3t.
- 3 π/8 1.18
- 3 π 9.42
- 3 π/2 4.71
- 6 π 18.85
Answer
C. 3 π/2 4.71
Solution
By symmetry, A=4 0π/2y≤ft|dx/dt |dt=4 0π/22 3t·6 2t t,dt=48 0π/2 4t 2t,dt=48·π/32=3π/2.
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