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:

Symbolism

The use of symbols to represent ideas or qualities in literature, art, and other forms of cultural expression.

Freud

Sigmund Freud, an Austrian neurologist and the founder of psychoanalysis, known for his theories of the unconscious mind, mechanisms of repression, and the role of sexual desires.

Id

In Freud’s theory, a term for the most primitive reactions of human personality, consisting of blind striving for immediate biological satisfaction regardless of cost.

Superego

In Freud’s theory, reaction patterns that emerge from within the ego, represent the internalized rules of society, and come to control the ego by punishment with guilt.