Find the Volume of the Solid Obtained by Rotating the Region

question 61

Multiple Choice

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. $y = \ln x , y = 1 , y = 5 , x = 0 ;$ about the $y -$ axis

• A) \(\frac { \pi } { 4 } \left( e ^ { 10 } - e \right)\)
• B) \(\frac { \pi } { 2 } \left( 1 - e ^ { 10 } \right)\)
• C) \(\frac { \pi } { 2 } \left( e ^ { 10 } - e ^ { 2 } \right)\)
• D) \(\frac { \pi e ^ { 10 } } { 2 }\)
• E) \(2 \pi \left( e ^ { 10 } - e ^ { 2 } \right)\)

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Definitions:

Double Coincidence

A situation in barter economies where two parties each possess an item the other wants, allowing for an exchange without the need for a common unit of value.

Small Denomination Time Deposits

Bank deposits that are held for a fixed term with a specified small minimum amount and earn interest over time.

Large Denomination Time Deposits

Time deposits in a bank or financial institution with a large minimum amount of money required, typically over $100,000, and a fixed term.

M2

A measure of the money supply that includes cash, checking deposits, and easily convertible near money, such as savings deposits, small time deposits, and money market mutual funds.