Given curve is an ellipse which is symmetric about X-axis both, as shown in the figure.
` :. ` Area bounded by ellipse
`=4xx` (area of shaded region in first quadrant)
`=4 xx int_(0)^(4)ydx`
`=4 int_(0)^(4)(3)/(4)sqrt(16-x^(2))dx`
`=3*int_(0)^(4)sqrt(4^(2)-x^(2))dx`
`=3[(x)/(2)sqrt(4^(2)-x^(2))+(4^(2))/(2)"sin"^(-1)((x)/(4))]_(0)^(4)`
`=3[2sqrt(16-16)+8"sin"^(-1)(1)-0-8sin^(-1)(0)]`
`=3[0+8"sin"^(-1)(1)-0]`
`=3xx8xx((pi)/(2))=12pi` sq. units.
