Evaluate the Iterated Integral by Converting to Polar Coordinates $$\int _ { - 5 } ^ { 5 } \int _ { 0 } ^ { \sqrt { 25 - y ^ { 2 } } } \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } d x d y .$$

question 152

Multiple Choice

Evaluate the iterated integral by converting to polar coordinates. Round the answer to two decimal places.
$$\int _ { - 5 } ^ { 5 } \int _ { 0 } ^ { \sqrt { 25 - y ^ { 2 } } } \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } d x d y .$$

• A) \(1963.5\)
• B) \(15.71\)
• C) \(4908.74\)
• D) \(39.27\)
• E) 625

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Definitions:

Effect Size Formula

A computational method used to quantify the strength of the relationship between two variables or the magnitude of difference between groups.

Population Standard Deviation

A measure of the amount of variation or dispersion of a set of values in a population.

Sample Size

The number of observations or entities considered in a statistical sample.

Standard Error

A measure of the statistical accuracy of an estimate, calculated from the standard deviation of a series of estimates.