question_answer

The area bounded by the curves\[y=|x|-1\]and\[y=-|x|+1\]is

A) \[1\,\,sq\,\,unit\]           

B)        \[2\,\,sq\,\,units\]

C) \[2\sqrt{2}sq\,\,units\]                

D) \[4\,\,sq\,\,units\]

Correct Answer: B

Solution :

The region is clearly square with vertices at the points\[(1,\,\,0),\,\,(0,\,\,1),\,\,(-1,\,\,0)\]and\[(0,\,\,-1)\]. So, its area\[=\sqrt{2}\times \sqrt{2}=2\]sq units.