If the Infinite Curve $y = e ^ { x } , x \geq 0$

question 92

Multiple Choice

If the infinite curve $y = e ^ { x } , x \geq 0$ , is rotated about the $x$ -axis, find the area of the resulting surface. Select the correct answer.

• A) \(\pi [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)
• B) \(\frac { \pi } { 3 } [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)
• C) \(\frac { \pi } { 6 } [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)
• D) \(\frac { \pi } { 6 } [ \sqrt { 3 } + \ln ( 1 + \sqrt { 3 } ) ]\)
• E) \(\frac { \pi } { 4 } [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)

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Definitions:

Consumption Expenditures

The total amount spent by households on goods and services for personal use within a specified period.

Investment Expenditures

Spending by businesses on capital goods, and by households on new homes.

Unemployment

A situation where individuals who are capable of working and willing to work do not find suitable employment.

Weather Patterns

The typical sequences or variations in meteorological conditions in a specific area over periods, which can impact various sectors including agriculture and energy.