Find the Length of the Curve $r = 3 \theta ^ { 2 } , 0 \leq \theta \leq 2 \sqrt { 3 }$

question 45

Multiple Choice

Find the length of the curve.
-The spiral $r = 3 \theta ^ { 2 } , 0 \leq \theta \leq 2 \sqrt { 3 }$

• A) \(\frac { 144 } { 5 } \pi ^ { 5 }\)
• B) \(8 \left( \left( \pi ^ { 2 } + 1 \right) ^ { 3 / 2 } - 1 \right)\)
• C) \(\frac { 1296 } { 5 } \sqrt { 3 }\)
• D) 56

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