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

question 151

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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