Evaluate $\int _ { C } \left[ 3 x ^ { 2 } y ^ { 2 } + 2 \cos ( 2 x + y ) \right] d x + \left[ 2 x ^ { 3 } y + \cos ( 2 x + y ) \right] d y$

Short Answer

Evaluate $\int _ { C } \left[ 3 x ^ { 2 } y ^ { 2 } + 2 \cos ( 2 x + y ) \right] d x + \left[ 2 x ^ { 3 } y + \cos ( 2 x + y ) \right] d y$ if C is the closed path starting at $( 0,0 )$ and moving clockwise around the square with vertices $( 0,0 )$ , $( 1,0 )$ , $( 1,1 )$ , and $( 0,1 )$ .