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

question 22

Multiple Choice

Set up, but do not evaluate, an integral for the length of the curve.
$y = 6 e ^ { x } \sin x , \quad 0 \leq x \leq \frac { 9 \pi } { 2 }$

• A) \(L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 - 36 e ^ { 2 x } ( 1 + \sin 2 x ) } d x\)
• B) \(L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 + 36 e ^ { 2 x } ( 1 + \sin 2 x ) } d x\)
• C)
• \(L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 - 36 e ^ { 2 x } ( 1 - \sin 2 x ) } d x\)
• D)
• \(L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 + 36 e ^ { 2 x } ( 1 - \sin 2 x ) } d x\)
• E)
• \[L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 + 36 e ^ { 2 x } ( 1 - \sin x ) } d x\]

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Definitions:

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