Evaluate the Line Integral $\int _ { C } \frac { x y } { 1 + x } d x - \ln ( 1 + x ) d y$

Short Answer

Evaluate the line integral $\int _ { C } \frac { x y } { 1 + x } d x - \ln ( 1 + x ) d y$ , where C is the triangular path consisting of the line segment from $( 0,0 )$ to $( 4,0 )$ , followed by the line segment from $( 4,0 )$ to $( 0,2 )$ , followed by the line segment from $( 0,2 )$ to $( 0,0 )$ .