Let the function $f ( x ) = x \sqrt [ 3 ] { \left( x ^ { 2 } - 1 \right) ^ { 2 } }$.
a) ( 0.75 points) Find $\lim _ { x \rightarrow 1 } \frac { f ( x ) } { ( x - 1 ) ^ { 2 / 3 } }$.
b) ( 1.75 points) Find the area, in the first quadrant, between the line $y = x$ and the graph of the function $f ( x )$.