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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Definitions:

Statistical Significance

Statistical significance is a determination that the observed results in data are not due to random chance, typically indicated by a p-value less than a predetermined threshold.

Hypothesized Reason

An assumed explanation or cause developed for the purpose of testing through research or experimentation.

Statistical Significance

Indicates that the observed results are unlikely to have occurred by chance, according to a predefined level of significance.

Type I Error

The statistical mistake of rejecting a true null hypothesis, also known as a "false positive."