question_answer

The area bounded by the curve \[y=\left\{ \begin{matrix}    {{x}^{2}}, & x<0  \\    x, & x\ge 0  \\ \end{matrix} \right.\] and the line \[y=4,\] is

A) \[\frac{32}{3}\]                                

B) \[\frac{8}{3}\]

C) \[\frac{40}{3}\]                                

D) \[\frac{16}{3}\]

Correct Answer: C

Solution :

 Given, curve \[y=\left\{ \begin{matrix}    {{x}^{2}},x<0  \\    x,x\ge 0  \\ \end{matrix} \right.\]and line\[y=4\]Area of \[OABO,\]