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

question 18

Multiple Choice

Set up, but do not evaluate, an integral for the length of the curve.
$$y = 2 e ^ { x } \sin x , \quad 0 \leq x \leq \frac { 3 \pi } { 2 }$$

• A)
• \(L = \int _ { 0 } ^ { 3 x / 2 } \sqrt { 1 - 4 e ^ { 2 x } ( 1 + \sin 2 x ) } d x\)
• B)
• \(L = \int _ { 0 } ^ { 3 x / 2 } \sqrt { 1 + 4 e ^ { 2 x } ( 1 - \sin x ) } d x\)
• C)
• \(L = \int _ { 0 } ^ { 3 x / 2 } \sqrt { 1 + 4 e ^ { 2 x } ( 1 - \sin 2 x ) } d x\)
• D)
• \(L = \int _ { 0 } ^ { 3 x / 2 } \sqrt { 1 - 4 e ^ { 2 x } ( 1 - \sin 2 x ) } d x\)
• E)
• \(L = \int _ { 0 } ^ { 3 x / 2 } \sqrt { 1 + 4 e ^ { 2 x } ( 1 + \sin 2 x ) } d x\)

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Definitions:

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Schemes designed to motivate and reward desired behaviors or performance from individuals or groups.

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A term used in decision theory referring to the actual but possibly unknown status of the world, which affects the outcomes of decisions.

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The cost of the next best alternative foregone as a result of making a decision.

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The realised gain from business operations or investments, after all costs and expenses have been deducted.