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

question 5

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:

Repression

In psychoanalytic theory, the basic defense mechanism that banishes from consciousness anxiety-arousing thoughts, feelings, and memories.

Long-Term Memory

The aspect of memory where information is stored for an extended period, ranging from hours to a lifetime.

Retrieval Failure

Occurs when memories are not accessible from long-term storage, often due to a lack of cues or interference from other information.

Anterograde Amnesia

A condition affecting memory, where after the onset of the amnesia, the affected individual is unable to form new memories, though long-term memories from before the event remain intact.