$\text { Find the area of the surface formed by revolving about the } \theta = \frac { \pi } { 2 } \text { axis the following }$

question 48

Multiple Choice

$\text { Find the area of the surface formed by revolving about the } \theta = \frac { \pi } { 2 } \text { axis the following }$ curve over the given interval. $r = e ^ { 8 \theta } , 0 \leq \theta \leq \frac { \pi } { 2 }$

• A) \(\frac { 2 \sqrt { 65 } \left( e ^ { 8 x } - 16 \right) \pi } { 385 }\)
• B) \(\frac { 2 \sqrt { 65 } \left( e ^ { 8 x } - 16 \right) \pi } { 257 }\)
• C) \(\frac { 2 \sqrt { 65 } \left( e ^ { 8 x } - 16 \right) \pi } { 129 }\)
• D) \(\frac { 2 \sqrt { 65 } \left( e ^ { 8 x } - 8 \right) \pi } { 129 }\)
• E) \(\frac { 2 \sqrt { 65 } \left( e ^ { 8 x } - 8 \right) \pi } { 257 }\)

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