The area (in square units) of minor segment of the circle x² + y² = 25 cut off by the line x = \(\frac{5}{2}\) is

\(\frac{25}{12}\)(4π - 3\(\sqrt {3 }\))

x² + y² = 25 and \(\frac{5}{2}\) $⇒y^2=25-x^2⇒y=\sqrt{25-x^2}$

$2\int_{\frac{5}{2}}^{5}\sqrt{25-x^2}$

$=2\begin{bmatrix}\frac{x}{2}\sqrt{25-x^2}+\frac{25}{2}sin^{-1}\frac{x}{5}\end{bmatrix}_{\frac{5}{2}}^{5}$

$\begin{Bmatrix}5×0+25×\frac{π}{2}\end{Bmatrix}-\begin{Bmatrix}\frac{5}{2}\sqrt{\frac{75}{4}}25×\frac{π}{6}\end{Bmatrix}$

$\frac{25π}{2}-\frac{25\sqrt{3}}{2}-\frac{25π}{6}=\frac{25π}{3×4}-\frac{25\sqrt{3}}{4×3}⇒\frac{25}{12}(4π-3\sqrt{3})$