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Find the area bounded by the parametric curve x = a cos³ t, y = b sin³ t together with the positive x-axis and positive y-axis.

1. πab/4
2. πab/32
3. 3πab/32
4. 5πab/32

Correct answer: 3πab/32

Solution

With x=a cos^3 t, y=b sin^3 t, the first-quadrant area = int_{pi/2}^{0} y (dx/dt) dt = 3ab*int_0^{pi/2} sin^4 t cos^2 t dt = 3*pi*a*b/32.

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