Find the Area of the Surface Obtained by Rotating the Curve

question 60

Short Answer

Find the area of the surface obtained by rotating the curve about the $x$ -axis.
$$x = \frac { 1 } { 3 } \left( y ^ { 2 } + 2 \right) ^ { \frac { 3 } { 2 } } , 1 \leq y \leq 2$$

---

Definitions:

Traditional Criteria

Established or long-standing principles and standards used to make decisions, evaluate performance, or define quality in various fields.

Standard Specification

Detailed and precise criteria set to describe the quality, material, and performance requirements of products, services, or processes.

Universal Specification

A set of guidelines or criteria designed to be applicable across a wide range of products, services, or industries.

Capital Assets

Long-term assets acquired or owned by a business or corporation that are used in the production of goods or services and are not expected to be consumed or converted into cash within a year.