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

---

Definitions:

Allied Powers

A coalition of countries, typically referring to those that opposed the Axis Powers during World War II, including the United States, the United Kingdom, the Soviet Union, and others.

World War II

A global conflict that lasted from 1939 to 1945, involving most of the world's nations, dubbed the deadliest conflict in human history.

Western Front

The main theatre of war during World War I, stretching from the North Sea to the Swiss border, where most of the fighting between Germany and the Allies occurred.

Yalta Conference

A 1945 meeting between Churchill, Roosevelt, and Stalin to discuss the post-World War II reorganization of Europe and the establishment of the United Nations.