Solve the Problem $y = \frac { 1 } { x ^ { 2 } }$

question 139

Multiple Choice

Solve the problem.
-The region between the curve $y = \frac { 1 } { x ^ { 2 } }$ and the $x$ -axis from $x = \frac { 1 } { 4 }$ to $x = 4$ is revolved about the $y$ -axis to generate a solid. Find the volume of the solid.

• A) \(2 \pi \ln 4 - \pi\)
• B) \(\pi \ln 4 - \pi\)
• C) \(4 \pi \ln 4\)
• D) \(2 \pi \ln 4\)

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Definitions:

Total Revenue

The total amount of money received by a firm from sales of its products or services, calculated as the quantity sold times the price per unit.

MC < MR

A condition in economic theory where marginal cost is less than marginal revenue, suggesting that increasing production would be profitable.

Profit Maximized

The point at which a firm achieves the highest possible profit margin, where marginal revenue equals marginal cost.

Total Cost

The overall expenditure incurred by a company in the production of goods or services, including fixed and variable costs.