Evaluate the Integral A) $\frac { 4 } { 9 } \pi ^ { 2 }$

question 53

Multiple Choice

Evaluate the integral.
- $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 2 \cos \varphi } \varrho ^ { 2 } \sin \varphi \mathrm { d } \varphi \mathrm { d } \theta \mathrm { d } \varphi$

• A) \(\frac { 4 } { 9 } \pi ^ { 2 }\)
• B) \(\frac { 1 } { 3 } \pi\)
• C) \(\frac { 4 } { 9 } \pi\)
• D) \(\frac { 1 } { 3 } \pi ^ { 2 }\)

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Definitions:

Main Connective

In logic, the operator that determines the overall value of a compound statement.

Symbolic Notation

Symbolic notation is the use of symbols and abbreviations to represent objects, operations, relations, and concepts, especially in mathematics and logic.

Atomic Statements

The simplest type of statements in logic that cannot be broken down into smaller components while retaining meaning.

Main Components

Key or primary parts that make up a system, machine, or composition.