Given equation of curve are

x = 3cost

=> x/3 = cost ........1

y = 2sint

=> y/2 = sint .........2

Square equation 1 and 2 and add the , we get

x² /9 + y² / 4 = sin² t + cos² t

=> x² /9 + y² / 4 = 1   (since sin² t + cos² t = 1 )

It is equation of an ellipse. So curve forms an ellipse.

Now area of ellipse = 4 *₀∫³  (2/3) *√(9 - x² ) dx

                             = (8/3) [(x/2) *√(9 - x² ) + (9/2) * sin^-1 (x/3) ₀]³   (Using formula of √(a² - x² ) )

                             = 6π 

So required area is 6π unit²