Use the Shell Method to Set Up and Evaluate the Integral

question 30

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 y-axis. $y = 14 x - x ^ { 2 } , x = 0 , y = 49$

• A) \(V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 49 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 6 } \pi\)
• B)\(V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 98 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 6 } \pi\)
• C)\(V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 196 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 6 } \pi\)
• D)\(V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 196 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 3 } \pi\)
• E)\(V = 2 \pi \int _ { 0 } ^ { 7 } x \left( 49 - \left( 14 x - x ^ { 2 } \right) \right) d x = \frac { 2,401 } { 3 } \pi\)

Grasp the various aspects and implications of global warming, including the large-scale relocation of species.

Comprehend the principles of sustainable development and its importance in balancing economic growth with environmental protection.

Recognize the historical and contemporary predictions regarding human population growth and carrying capacity, including the views of Thomas Malthus.

Acquire insights into the role and focus of environmental sociology as a discipline.

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Definitions:

Acquiring Firm

A company that purchases another company in a merger or acquisition to expand its operations or enter new markets.

Bankruptcy Judge

A judicial officer who presides over court proceedings in bankruptcy cases, making decisions on matters within the bankruptcy law.

Disbursements

Payments made by a business, including operating expenses, dividend payments, and investments in assets.

Trustee

With respect to bonds, an organization that ensures compliance with the conditions set forth in the indenture. With respect to bankruptcy, a person who administers the bankrupt organization to ensure funds are properly handled.