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

Short Answer

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