Solve the Problem $f ( x , y ) = \sin \sqrt { x ^ { 2 } + y ^ { 2 } }$

Multiple Choice

Solve the problem.
-Integrate $f ( x , y ) = \sin \sqrt { x ^ { 2 } + y ^ { 2 } }$ over the region $0 \leq x ^ { 2 } + y ^ { 2 } \leq 16$ .

A) $\pi ( \sin 4 - \cos 4 )$
B) $\pi ( \sin 4 - 4 \cos 4 )$
C) $2 \pi ( \sin 4 - \cos 4 )$
D) $2 \pi ( \sin 4 - 4 \cos 4 )$