Verify Green's Theorem by Evaluating Both Integrals For the Path $C$

Multiple Choice

Verify Green's Theorem by evaluating both integrals $\int _ { c } 14 y ^ { 2 } d x + 14 x ^ { 2 } d y = \int _ { R } \int \left( \frac { \partial N } { \partial x } - \frac { \partial M } { \partial y } \right) \partial A$ for the path $C$ defined as the boundary of the region lying between the graphs of $y = x$ and $y = x ^ { 2 }$ .

A) $\frac { 42 } { 5 }$
B) $\frac { 21 } { 5 }$
C) $\frac { 7 } { 3 }$
D) $\frac { 28 } { 15 }$
E) $\frac { 7 } { 15 }$