question_answer

The area (in sq. units) of the region \[\{(x,y)\}:x\ge 0,x+y\le 3,{{x}^{2}}\le 4y\]and \[y\le 1+\sqrt{x}\}\]is:                       JEE Main Solved Paper-2017

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

B)  \[\frac{59}{12}\]

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

D)  \[\frac{7}{3}\]

Correct Answer: A

Solution :

\[\text{Area}=\int\limits_{0}^{1}{(1+\sqrt{x})}dx+\int\limits_{1}^{2}{(3-x)}dx-\int\limits_{0}^{2}{\frac{{{x}^{2}}}{4}}dx\] \[=\frac{5}{2}\]