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athematics The area (in sq. units ) of the region described by [JEE Main Solved Paper-2015 ]

A) \[\frac{15}{64}\]                                              

B) \[\frac{9}{32}\]

C) \[\frac{7}{32}\]                                

D) \[\frac{5}{64}\]

Correct Answer: B

Solution :

The required region is shown shaded. The points of intersections are\[\left( \frac{1}{8},-\frac{1}{2} \right)\And \left( \frac{1}{2},1 \right)\] \[\Rightarrow \]Required area\[=\int\limits_{-\frac{1}{2}}^{1}{\left( \frac{y+4}{4}-\frac{{{y}^{2}}}{2} \right)dy=\frac{9}{32}}\]