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

question 6

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) \(\pi \left( 1 - e ^ { - 729 / 2 } \right)\)

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