Find the Exact Area of the Surface Obtained by Rotating $x$

question 132

Short Answer

Find the exact area of the surface obtained by rotating the given curve about the $x$ -axis.
$$x = 2 \cos ^ { 3 } \theta , \quad y = 2 \sin ^ { 3 } \theta , \quad 0 \leq \theta \leq \pi / 2$$

---

Definitions:

Intangible

Assets that lack physical substance but hold value for a firm, such as patents, trademarks, and goodwill.

Commercial Substance

An aspect of transactions indicating that it will result in a significant change in the economic circumstances of the participating entities.

Realized Gain

The profit earned from the sale of an asset, calculated as the difference between the asset's sale price and its original purchase price.

Income Statement

A report detailing a corporation's income, costs, and earnings within a given timeframe.