Evaluate the Iterated Integral $\int _ { 0 } ^ { 2 x } \int _ { 0 } ^ { 1 } \int _ { 1 - y ^ { 2 } } ^ { 4 } r ^ { 2 } d z d r d \theta$

question 47

Multiple Choice

Evaluate the iterated integral $\int _ { 0 } ^ { 2 x } \int _ { 0 } ^ { 1 } \int _ { 1 - y ^ { 2 } } ^ { 4 } r ^ { 2 } d z d r d \theta$ .

• A) \(\frac { \pi } { 5 }\)
• B) \(\frac { 7 \pi } { 5 }\)
• C)4\(\pi\)
• D)12\(\pi\)
• E) \(\frac { \pi } { 16 }\)
• F) \(\frac { \pi } { 2 }\)
• G) \(\frac { 12 \pi } { 3 }\)
• H) \(\frac { 12 \pi } { 5 }\)

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Definitions:

Direct Labor-Hours

Complete work hours of employees directly incorporated in production tasks.

Variable Overhead

Indirect production costs that vary with the level of production, such as electricity costs or materials used in the maintenance of machinery.

Manufacturing Overhead

All indirect costs associated with manufacturing, such as indirect materials, indirect labor, and other overhead costs.

Labor Efficiency Variance

The difference between the actual labor hours used and the standard labor hours expected, multiplied by the standard labor rate.