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

question 173

Multiple Choice

Change the Cartesian integral to an equivalent polar integral, and then evaluate.
- $\int _ { - 4 } ^ { 4 } \int _ { - \sqrt { 16 - y ^ { 2 } } } ^ { \sqrt { 16 - y ^ { 2 } } } \ln \left( x ^ { 2 } + y ^ { 2 } + 1 \right) d x d y$

• A) \(\pi ( 16 \ln 17 + 16 )\)
• B) \(\pi ( 17 \ln 17\) - 16)
• C) \(\pi ( 16 \ln 17 - 16 )\)
• D) \(\pi ( 17 \ln 17 + 16 )\)

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Definitions:

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Particles that possess energy significantly greater than average, often referring to subatomic particles such as protons, neutrons, and cosmic rays.

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A measurement unit for the thermal energy accumulated, used in forensic entomology to estimate the time since death based on insect development.

Chemiluminescence

The emission of light (luminescence) as the result of a chemical reaction without the need for external light sources.

Homogeneous Catalyst

A catalyst that exists in the same phase (solid, liquid, or gas) as the reactants in a chemical reaction, promoting the reaction without being consumed.