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

• A

  $\frac{\pi^2}{5}$ sq unit
• B

  $\frac{\pi^2}{2}$ sq unit
• Correct answer
  C

  $\left(\frac{\pi}{4}-\frac{1}{2}\right)$ sq unit
• D

  $\frac{\pi}{4}$ sq unit

Solution

Required area $=\frac{1}{4}($ Area of circle $)-($ Area of $\triangle A O B)$ $\begin{aligned} & =\frac{\pi(1)^2}{4}-\frac{1}{2} \times O A \times O B \\ & =\left(\frac{\pi}{4}-\frac{1}{2}\right) \text { sq unit }\end{aligned}$

Hence, the correct answer is option: 'C'.