Up and Evaluate the Double Integral $\int _ { R } \int f ( x , y ) d A$

Multiple Choice

$$\text { Given } f ( x , y ) = e ^ { - \left( x ^ { 2 } + y ^ { 2 } \right) / 2 } , R : x ^ { 2 } + y ^ { 2 } \leq 729 , x \geq 0 \text {, use polar coordinates to set }$$ up and evaluate the double integral $\int _ { R } \int f ( x , y ) d A$ .

A) $\pi \left( 1 - e ^ { - 19683 / 2 } \right)$
B) $\left( 1 + e ^ { - 729 / 2 } \right)$
C) $\pi \left( 1 + e ^ { - 19683 / 2 } \right)$
D) $\left( 1 - e ^ { - 729 / 2 } \right)$
E) $\pi \left( 1 - e ^ { - 729 / 2 } \right)$