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Question

The area enclosed by the curves x=asin3t and y=acos3t is equal to

A
12a2π/20cos4t sin2t dt
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B
12a2π/20cos2t sin4t dt
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C
2aa(a23x23)32dx
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D
4a0(a23x23)32dx
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Solution

The correct options are
A 12a2π/20cos4t sin2t dt
C 2aa(a23x23)32dx
D 4a0(a23x23)32dx
Eliminating t, we have
x23+y23=a23
y=(a2/3x2/3)3/2
From the figure,
A=2aa(a2/3x2/3)3/2 dx
=4a0(a2/3x2/3)3/2 dx
=4a0y dx
=4a2π/203cos3t sin2t cost dt

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