Solve the Problem $x$ -Axis, the Curve $y = \sqrt { \frac { 7 x } { x ^ { 2 } + 1 } } , x = 1$

question 126

Multiple Choice

Solve the problem.
-Find the volume of the solid that is generated by revolving the area bounded by the $x$ -axis, the curve $y = \sqrt { \frac { 7 x } { x ^ { 2 } + 1 } } , x = 1$ , and $x = 8$ about the $x$ -axis.

• A) \(7 \pi \ln \left( \frac { 65 } { 2 } \right)\)
• B) \(\frac { 7 } { 4 } \pi \ln \left( \frac { 65 } { 2 } \right)\)
• C) \(\frac { 7 } { 2 } \pi \ln \left( \frac { 65 } { 2 } \right)\)
• D) \(\frac { 7 } { 2 } \ln \left( \frac { 65 } { 2 } \right)\)

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Definitions:

ADP

Adenosine diphosphate, a molecule involved in energy transfer within cells and plays a crucial role in metabolism.

NADPH

A coenzyme involved in anabolic reactions, such as lipid and nucleic acid synthesis, and provides the reducing power needed for the biosynthetic processes in cells.

Exergonic Reaction

A chemical reaction that releases energy to the surroundings, typically in the form of heat.

Free Energy

A thermodynamic quantity that represents the amount of energy in a system available to do work, often symbolized as G.