question_answer

Area of the region bounded by  \[\{(x,y);{{x}^{2}}+{{y}^{2}}\le 1\le x+y\}\] is equal to

A)  \[\frac{{{\pi }^{2}}}{5}\]                               

B)  \[\frac{{{\pi }^{2}}}{2}\]

C)  \[\frac{\pi }{4}+\frac{1}{2}\]                           

D)  \[\frac{\pi }{4}-\frac{1}{2}\]

Correct Answer: D

Solution :

Area of shaded region \[=\frac{\pi {{(1)}^{2}}}{4}\,-\frac{1}{2}\,(1)(1)\,=\frac{\pi }{4}\,-\frac{1}{2}\]