Use Green's Theorem And/or a Computer Algebra System to Evaluate $\int _ { C } x ^ { 2 } y d x - x y ^ { 2 } d y$

Multiple Choice

Use Green's Theorem and/or a computer algebra system to evaluate $\int _ { C } x ^ { 2 } y d x - x y ^ { 2 } d y$ , where $C$ is the circle $x ^ { 2 } + y ^ { 2 } = 64$ with counterclockwise orientation.

A) $8 \pi$
B) $64 \pi$
C) $2 \pi$
D) $- 32 \pi$
E) None of these