Find the Volume of the Solid Generated by Revolving the Region

question 49

Multiple Choice

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve $y = e ^ { - 2 x }$ , and the line $x = 2$ about the $y$ -axis.

• A) \(\frac { 1 } { 2 } \pi \left( 1 - 5 \mathrm { e } ^ { - 4 } \right)\)
• B) \(\frac { 1 } { 2 } \pi \left( 1 - 3 \mathrm { e } ^ { - 4 } \right)\)
• C) \(\frac { 1 } { 2 } \pi \left( 1 - 4 \mathrm { e } ^ { - 4 } \right)\)
• D - \(\frac { 1 } { 2 } \pi \left( 1 + 5 e ^ { - 4 } \right)\)

---

Definitions:

Knowledge Sharing

The dissemination and exchange of information, skills, and expertise within and between individuals, teams, or organizations.

Constant Improvement

The ongoing process of making enhancements and optimizations to achieve better outcomes.

Consumer Trust

The confidence and belief that consumers have in the reliability and integrity of a brand or product.

Mattel

A large, multinational toy manufacturing company known for iconic brands such as Barbie, Hot Wheels, and Fisher-Price.