Use the Shell Method to Set Up and Evaluate the Integral

question 27

Multiple Choice

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. $y = x ^ { 6 } , x = 0 , y = 64$

• A) \(V = 2 \pi \int _ { 0 } ^ { 64 } y \left( y ^ { \frac { 1 } { 6 } } \right) d y = \frac { 98,304 } { 13 } \pi\)
• B) \(V = 2 \pi \int _ { 0 } ^ { 64 } y \left( y ^ { - \frac { 1 } { 6 } } \right) d y = \frac { 49,152 } { 13 } \pi\)
• C) \(V = 2 \pi \int _ { 0 } ^ { 64 } y \left( y ^ { \frac { 1 } { 6 } } \right) d y = \frac { 24,576 } { 13 } \pi\)
• D) \(V = 2 \pi \int _ { 0 } ^ { 64 } y \left( y ^ { \frac { 1 } { 6 } } \right) d y = \frac { 48,384 } { 13 } \pi\)
• E)\(V = 2 \pi \int _ { 0 } ^ { 64 } y \left( y ^ { \frac { 1 } { 6 } } \right) d y = \frac { 768 } { 13 } \pi\)

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Definitions:

Current Ratio

A liquidity ratio that measures a company's ability to pay off its short-term liabilities with its short-term assets.

Acid-Test Ratio

A financial metric comparing a company's most liquid assets (excluding inventory) to its current liabilities, used to assess short-term solvency.

Marketable Securities

These are liquid financial instruments that can easily be converted into cash at their current value in the financial markets.

Selling And Administrative Expenses

Expenses related to the selling of products and the management of the business, not directly tied to manufacturing.