Question

Area of the region bounded by $\left[\right(x,y):x^2+y^2\le 1\le x+y]$ is equal to

• A. $\frac{{\pi }^2}{5}$
• B. $\frac{{\pi }^2}{2}$
• C. $\frac{\pi }{4}+\frac{1}{2}$
• D. $\frac{\pi }{4}-\frac{1}{2}$

Answer 1

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

Area of shaded region
$=\frac{\pi (1{)}^2}{4}-\frac{1}{2}\left(1\right)\left(1\right)=\frac{\pi }{4}-\frac{1}{2}Ans.$
$Aliter:Circle{x}^2+y^2\le 1$
$Linex+y\ge 1$.
$\therefore Area:={\int }_0^1(\sqrt{1-x^2}dx-(1-x\left)\right)dx$
$=\frac{\pi }{4}-\frac{1}{2}Ans.$