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:

Free-Living Bacterium

A free-living bacterium is one that exists independently in the environment, not requiring a host organism for survival.

Pseudogenes

Segments of DNA that are similar to functional genes but are non-functional due to mutations, representing evolutionary remnants.

Mobile Elements

Sequences of DNA that can move or copy themselves to new positions within the genome of a single cell.

Evolution Rate

The speed at which evolutionary changes occur within a species or across species, influenced by various environmental and genetic factors.