Evaluate $\int _ { C } \mathbf { F } d \mathbf { r }$

Evaluate $\int _ { C } \mathbf { F } d \mathbf { r }$ where $\mathbf { F } ( x , y ) = \left( e ^ { x ^ { 2 } } - y ^ { 3 } , \cos y ^ { 2 } + x ^ { 3 } \right)$ and the curve C is given by C : $x = 2 \sin t , y = 2 \cos t , 0 \leq t \leq 2 \pi$ .

A) $24 \pi$
B) $12 \pi$

C) $48 \pi$
D) $96 \pi$
E) $- 24 \pi$
F) $- 12 \pi$
G) $- 48 \pi$

H) $0$

Correct Answer:

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