AOB is the positive quadrant of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ in which OA = a and OB = b. Find the area between the chord AB and the arc AB of the ellipse is $\frac{1}{4}ab(π-2)$:

$\frac{1}{4}(ab)(π-2)$

Shaded Area = $\int\limits_0^ab\sqrt{1-\frac{x^2}{a^2}}dx-\int\limits_0^ab(1-\frac{x}{a})dx$

$=\frac{1}{4}(ab)(π-2)$