Question

The area of the region $\left\{\right(x,y):x^2+y^2\le 1\le x+y\}$ is

• A. $\frac{{\pi }^2}{2}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{4}-\frac{1}{2}$
• D. $\frac{{\pi }^2}{3}$

Answer 1

The correct option is C $\frac{\pi }{4}-\frac{1}{2}$

Required area(shaded)$=\frac{1}{4}\text{(area of circle)}-\text{area}\left(\Delta AOB\right)=\frac{1}{4}\cdot \pi (1{)}^2-\frac{1}{2}\cdot 1\cdot 1=\frac{\pi }{4}-\frac{1}{2}\text{sq.units.}$