Solve the Problem $x$ -Axis and the Curve $y = \sin 6 x , 0 \leq x \leq \pi / 6$

question 143

Multiple Choice

Solve the problem.
-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the $x$ -axis and the curve $y = \sin 6 x , 0 \leq x \leq \pi / 6$ about the line $x = \pi / 6$ .

• A) \(\frac { \pi ^ { 2 } } { 36 }\)
• B) \(\frac { 1 } { 18 } \pi ^ { 2 }\)
• C) \(\frac { 1 } { 18 } \pi\)
• D) \(\frac { 1 } { 18 } \pi ^ { 2 } - \pi\)

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Definitions:

Sublimation

A defense mechanism in psychoanalytic theory where socially unacceptable impulses or idealizations are unconsciously transformed into socially acceptable actions or behavior.

Repression

A defense mechanism where unpleasant thoughts, desires, or experiences are excluded from conscious awareness.

Libido

The energy of the sexual drive as a component of the life instinct.

Life Instinct

, in psychoanalytic theory, represents the drive for survival, propagation, love, and creativity.