question_answer

The area of the region \[A=\{(x,\,\,y):0\,\,\le \,\,y\,\,\le \,\,x|x|+1\,\,and\,\,-\,1\le x\le 1\}\]in sq. units, is : [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) \[\frac{4}{3}\]                                      

B)               \[\frac{1}{3}\]     

C)               \[\frac{2}{3}\]                                      

D)               2

Correct Answer: D

Solution :

Required area \[=\,\,\,\int\limits_{-1}^{1}{\left( x\left| x \right|+1 \right)dx}\] \[=0+{{\left( x \right)}^{1}}_{-1}=2\]