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

question 58

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.)
$$y = \frac { 2 } { x } \text { on } [ 4,5 ]$$

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