Let C be the closed path from $( 0,0 )$ to $( 2,4 )$ along $y = x ^ { 2 }$ and back again from $( 2,4 )$ to $( 0,0 )$ along $y = 2 x$ . Evaluate $\int _ { C } \left( x ^ { 3 } + 2 y \right) d x + \left( x - y ^ { 2 } \right) d y$ directly, and then using Green's Theorem.

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The Answer of Let C be the closed path from $( 0,0 )$ to $( 2,4 )$ along $y = x ^ { 2 }$ and back again from $( 2,4 )$ to $( 0,0 )$ along $y = 2 x$ . Evaluate $\int _ { C } \left( x ^ { 3 } + 2 y \right) d x + \left( x - y ^ { 2 } \right) d y$ directly, and then using Green's Theorem.

Let C Be the Closed Path From (0,0)( 0,0 )(0,0) To (2,4)( 2,4 )(2,4)

Let C Be the Closed Path From $( 0,0 )$ To $( 2,4 )$