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)
• \[\int _ { 1 } ^ { 5 } 2 \pi ( 5 x ) \sqrt { 1 + \left( \frac { 5 } { x } \right) ^ { 2 } } d x\]