Area of region bounded by circle and axis/chord forms via integration setup for JEE

Formula

\[\text{If } x^2+y^2=a^2,\ \text{then upper semicircle } y=\sqrt{a^2-x^2},\ \text{and area }=\int (\text{top}-\text{bottom})\,dx\]

Variables: \(a\) is radius.

Conditions: Split using symmetry when convenient.

Circle segment and semicircle area problems.