Change the Cartesian Integral to an Equivalent Polar Integral, and Then

question 419

Multiple Choice

Change the Cartesian integral to an equivalent polar integral, and then evaluate.
- $$\int _ { 0 } ^ { 9 } \int _ { 0 } ^ { \sqrt { 81 - x ^ { 2 } } } e ^ { - \left( x ^ { 2 } + y ^ { 2 } \right) } d y d x$$

• A) \(\frac { \pi \left( 1 - e ^ { - 81 } \right) } { 2 }\)
• B) \(\frac { \pi \left( 1 - \mathrm { e } ^ { - 81 } \right) } { 4 }\)
• C) \(\frac { \pi \left( 1 + \mathrm { e } ^ { - 81 } \right) } { 4 }\)
• D) \(\frac { \pi \left( 1 + \mathrm { e } ^ { - 81 } \right) } { 2 }\)

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