AOB is the positive quadrant of the ellipse ${\mathrm{x}}^2/{\mathrm{a}}^2+{\mathrm{y}}^2/{\mathrm{b}}^2=1,$ where OA=a,OB=b.The area between the arc AB and the chord AB of the ellipse is

$\text{ Area of ellipse is }\pi ab\text{. Then the area of ellipse in the first }$$\text{ quadrant is }\frac{1}{4}\pi ab\text{ sq. units. }$

$\text{ Now area of triangle }OAB=\frac{1}{2}ab\text{ sq. units }$

$\text{ Hence, the required area is }\frac{1}{4}\pi ab-\frac{1}{2}ab=\frac{ab}{4}(\pi -2)\text{ sq. units. }$