question_answer

Let f(x) be a continuous function given by\[f(x)=\left\{ \begin{matrix}    2x, & |x|\underline{<}\,\,1  \\    {{x}^{2}}+ax+b, & |x|\,\,>1  \\ \end{matrix} \right\}\]. Find the area of the region in the third quadrant bounded by the curves \[x=-2{{y}^{2}}\] and \[y=f\left( x \right)\]lying on the left of the line \[8x+1=0.\]

A)  \[\frac{257}{192}sq\,\,unit\]      

B)  \[\frac{389}{175}sq\,\,unit\]

C)  \[\frac{382}{125}sq\,\,unit\]                  

D)  \[\frac{157}{192}sq\,\,unit\]

E)  None of these