If R Is the Region Bounded By $x ^ { 2 } + y ^ { 2 } = 4 , x ^ { 2 } + y ^ { 2 } = 9$

Multiple Choice

If R is the region bounded by $x ^ { 2 } + y ^ { 2 } = 4 , x ^ { 2 } + y ^ { 2 } = 9$ then $\iint$ _R $\left( x ^ { 2 } + y \right) d A$ in polar form is

A) $\int _ { 0 } ^ { 2 \pi } \left[ \int _ { 2 } ^ { 3 } r \left( r \cos ^ { 2 } \theta + \sin \theta \right) d r \right] d \theta$
B) $\int _ { 0 } ^ { 2 \pi } \left[ \int _ { 2 } ^ { 3 } r ^ { 2 } \left( r \cos ^ { 2 } \theta + \sin \theta \right) d r \right] d \theta$
C) $\int _ { 0 } ^ { \pi } \left[ \int _ { 2 } ^ { 3 } r ^ { 2 } \left( r \cos ^ { 2 } \theta + \sin \theta \right) d r \right] d \theta$
D) $\int _ { 0 } ^ { \pi } \left[ \int _ { 2 } ^ { 3 } r \left( r \cos ^ { 2 } \theta + \sin \theta \right) d r \right] d \theta$
E) $\int _ { - \pi } ^ { \pi } \left[ \int _ { 2 } ^ { 3 } r ^ { 2 } \left( r \cos ^ { 2 } \theta + \sin \theta \right) d r \right] d \theta$