Find the Volume of the Solid Obtained by Rotating About $y$

question 95

Multiple Choice

Find the volume of the solid obtained by rotating about the $y$ axis the region bounded by the curves.
$y = e ^ { - x ^ { 2 } } , y = 0 , x = 0$ and $x = 9$

• A) \(V = \pi \left( \frac { 1 } { e ^ { 81 } } \right)\)
• B)
• \(V = \pi \left( 1 - \frac { 1 } { e ^ { 81 } } \right)\)
• C) \(V = \pi e ^ { 81 }\)
• D) \( \pi \left( \frac { 1 } { e ^ { 81 } } - 1 \right)\)
• E) \(V = \pi \left( e ^ { 81 } - 1 \right)\)

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Definitions:

Standard Of Living

The amount of riches, convenience, possessions, and basic requirements afforded to a person, collective, or civilization.

Birthrate

is measured as the number of live births per thousand people in a population per year, indicating the rate at which a population is growing or declining.

Population

The total number of individuals or inhabitants in a specific area or region at a certain time.

Principle Of Population

A theory suggesting that population growth is potentially exponential while the growth of the food supply or other resources is linear.