Set Up an Integral for the Area of the Surface $$y = x ^ { 3 } , 0 \leq x \leq 2 ; x \text {-axis }$$

question 69

Multiple Choice

Set up an integral for the area of the surface generated by revolving the given curve about the indicated axis.
- $$y = x ^ { 3 } , 0 \leq x \leq 2 ; x \text {-axis }$$

• A) \(2 \pi \int _ { 0 } ^ { 2 } x ^ { 3 } \sqrt { 1 + 9 x ^ { 4 } } d x\)
• B) \(\pi \int _ { 0 } ^ { 2 } x ^ { 2 } \sqrt { 1 + 9 x ^ { 4 } } d x\)
• C) \(\pi \int _ { 0 } ^ { 2 } x ^ { 3 } \sqrt { 1 + 9 x ^ { 4 } } d x\)
• D) \(2 \pi \int _ { 0 } ^ { 2 } x ^ { 2 } \sqrt { 1 + 9 x ^ { 4 } } d x\)

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Definitions:

Standard Machine Setups

Predetermined procedures and settings used to configure machinery for production runs, aimed at optimizing efficiency and quality.

Variable Manufacturing Overhead

Variable manufacturing overhead consists of production costs that fluctuate with the level of output, such as utilities and materials used in the production process.

Variable Overhead Rate Variance

The difference between the actual variable overhead rate incurred during a period and the standard variable overhead rate, multiplied by the actual activity level.

Variable Overhead Rate Variance

The difference between the actual variable overhead incurred and the standard cost allocated based on the actual levels of the allocation base.