question_answer

Let \[A=\{(x,y):{{y}^{2}}\le 4x,y-2x\ge -4\}.\]The area (in square units) of the region A is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )

A) 8                                             

B) 9

C) 10                                          

D) 11

Correct Answer: B

Solution :

Area of shaded portion \[=\left| \int_{2}^{4}{\left( \frac{y+4}{2} \right)dy} \right|-\left| \int_{-2}^{4}{\frac{{{y}^{2}}}{4}dy} \right|\] \[=\left| \frac{1}{2}\left[ \frac{{{y}^{2}}}{2}+4y \right]_{-2}^{4} \right|-\left| \frac{1}{4}\left[ \frac{{{y}^{3}}}{3} \right]_{-2}^{4} \right|\] \[=\left| \frac{1}{2}\left[ \{8+16\}-\{2-8\} \right] \right|-\left| \frac{1}{4}\left\{ \frac{64}{3}+\frac{8}{3} \right\} \right|\] = 15 ? 6 = 9 sq units