Evaluate the Surface Integral of G Over the Surface S $S$

question 219

Multiple Choice

Evaluate the surface integral of G over the surface S.
- $S$ is the parabolic cylinder $y = 3 x ^ { 2 } , 0 \leq x \leq 2$ and $0 \leq z \leq 4 ; G ( x , y , z ) = 3 x$

• A) \(\frac { 1 } { 9 } ( 145 \sqrt { 145 } - 1 )\)
• B) \(\frac { 1 } { 3 } ( 145 \sqrt { 145 } - 1 )\)
• C) \(\frac { 1 } { 9 } ( 145 \sqrt { 145 } + 1 )\)
• D) \(\frac { 1 } { 3 } ( 145 \sqrt { 145 } + 1 )\)

---

Definitions:

Confidence Interval

A statistical range that estimates where a population parameter lies with a certain probability.

Sample Standard Deviations

A measure that quantifies the amount of variation or dispersion of a set of sample data values.

Margin Of Error

An estimate of the amount by which a sample statistic differs from a population parameter, expressed often as a confidence interval.

Equal Sample Sizes

A condition in statistical analysis where the number of data points or observations in each group or category being compared is the same.