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) \(2 \pi \int _ { 1 } ^ { 5 } \frac { 2 } { x } \left( 1 + \left( - \frac { 2 } { x ^ { 2 } } \right) ^ { 2 } \right) d x\)

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Definitions:

Control

In experimental research, the standard that the experiment is compared against. It can also refer to the power to influence or direct people's behavior or the course of events.

Motor Development Sequence

The progression of physical skills that infants and children develop as they gain muscle control and coordination.

Proximodistal Trend

A pattern of growth and development where movements at the body's center occur before those at the periphery (limbs, fingers).

Cephalocaudal Trend

A developmental pattern in humans where growth and motor skill development proceed from the head downward through the body.