Evaluate the Line Integral $\int _ { C } \left( 2 x y ^ { 2 } + \tan ^ { - 1 } x ^ { 3 } \right) d x + \left( x ^ { 2 } y + \sqrt { y ^ { 3 } + 1 } \right) d y$

Short Answer

Evaluate the line integral $\int _ { C } \left( 2 x y ^ { 2 } + \tan ^ { - 1 } x ^ { 3 } \right) d x + \left( x ^ { 2 } y + \sqrt { y ^ { 3 } + 1 } \right) d y$ , where C consists of the arc of the parabola $y = x ^ { 2 }$ from $( 1,1 )$ to $( 2,4 )$ , followed by the line segments from $( 2,4 )$ to $( 0,4 )$ , from $( 0,4 )$ to $( 0,1 )$ and from $( 0,1 )$ to $( 1,1 )$ .