Area of shaded region = 2 x Area of region OABO.
Now, length of strip = 3 - x = \(\frac{3-y^2}{4}\)
(∵ at area x = \(\frac{y^2}{4}\))
let breadth of strip = dy
∴ Area of strip = \(\Big(\frac{3-y^2}{4}\Big)\)dy.
Since in region OABO , the strip is vegion from line y = 0 to y = 2√3.
∴ Area of vegion OABO = 0∫2√3\(\Big(\frac{3-y^2}{4}\Big)\)dy
= \(\Big(3y-\frac{y^3}{12}\Big)^{2\sqrt{3}}_0\)
= 6√3 - \(\frac{24\sqrt{3}}{12}\)
= 6√3 - 2√3
= 4√3 sq.units
∴ Area of shaded region = 2 x 4√3
= 8√3 sq.units.
