Write an Integral Giving the Area of the Surface Obtained $x$

question 53

Multiple Choice

Write an integral giving the area of the surface obtained by revolving the curve about the $x$ -axis. (Do not evaluate the integral.)
$$y = \frac { 2 } { x } \text { on } [ 1,5 ]$$

• A)\(2 \pi \int _ { 1 } ^ { 5 } \frac { \sqrt { x ^ { 4 } - 4 } } { x ^ { 3 } } d x\)
• B) \(4 \pi \int _ { 1 } ^ { 5 } x ^ { 3 } \sqrt { x ^ { 4 } + 4 } d x\)
• C) \(4 \pi \int _ { 1 } ^ { 5 } \frac { \sqrt { x ^ { 4 } + 4 } } { x ^ { 3 } } d x\)
• D) \(2 \pi \int _ { 1 } ^ { 5 } \frac { 2 } { x } \left( 1 + \left( - \frac { 2 } { x ^ { 2 } } \right) ^ { 2 } \right) d x\)

Identify the concept of mood linkage and its effects on social environments.

Understand the preservation of innovation through cultural practices.

Identify key historical terms and their significance within early American history.

Understand the impact of European colonization on Indigenous populations.

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Definitions:

Nonrenewable Resources

Resources that cannot be replenished at the same rate they are consumed, such as oil, coal, and natural gas.

Recycling

The process of converting waste materials into new products to prevent waste of potentially useful materials.

Efficient Use

The optimal allocation and utilization of resources to achieve a particular goal or outcome with minimal waste or expense.

Restoration Ecology

Seeks scientific ways to return ecosystems to their state prior to habitat degradation.