Set Up, but Do Not Evaluate, an Integral for the Area

question 2

Multiple Choice

Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve $y = \ln x ^ { 5 }$ about the $x$ -axis on the interval $1 \leq x \leq 5$ .

• A)
• \[\int _ { 5 } ^ { 1 } 2 \pi x \ln ( x ) \sqrt { 1 + \left( \frac { 5 } { x } \right) ^ { 2 } } d x\]
• B)
• \[\int _ { 5 } ^ { 1 } 2 \pi \sqrt { 1 + \left( \frac { 5 } { x } \right) ^ { 2 } } d x\]
• C)
• \[\int _ { 1 } ^ { 5 } 2 \pi ( 5 \ln ( x ) ) \sqrt { 1 + \left( \frac { 5 } { x } \right) ^ { 2 } } d x\]
• D)
• \[\int _ { 5 } ^ { 1 } 2 \pi ( 5 x ) \sqrt { 1 + \left( \frac { 5 } { x } \right) ^ { 2 } } d x\]
• E)
• \[\int _ { 1 } ^ { 5 } 2 \pi ( 5 x ) \sqrt { 1 + \left( \frac { 5 } { x } \right) ^ { 2 } } d x\]

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Definitions:

Estimated Trips

The projected number of journeys or movements, in transportation planning, based on factors such as population, land use, or economic activity.

Terminal Distance

The total distance from the beginning to the end of a process, pathway, or transportation route.

Trips

The act of going from one place to another, often implying a short journey for a specific purpose or task.