Evaluate the Line Integral by Two Methods: Directly and Using $\oint _ { C } x d x - x ^ { 2 } y ^ { 2 } d y$

Short Answer

Evaluate the line integral by two methods: directly and using Green's Theorem. $\oint _ { C } x d x - x ^ { 2 } y ^ { 2 } d y$ , where C is the triangle with vertices $( 0,0 )$ , $( 1,1 )$ , and $( 0,1 )$ .