Solve the Problem $C : ( f ( u ) , g ( u ) )$

question 196

Essay

Solve the problem.
-Suppose that the parametrized plane curve $C : ( f ( u ) , g ( u ) )$ is revolved about the $x$ -axis, where $g ( u ) > 0$ and a $\leq u \leq$ b. Show that the surface area of the surface of revolution is $2 \pi \int _ { a } ^ { b } g ( u ) \sqrt { \left[ g ^ { \prime } ( u ) \right] ^ { 2 } + \left[ f ^ { \prime } ( u ) \right] ^ { 2 } } \mathrm { du }$

---

Definitions:

Ideological Reasoning

The practice of interpreting or justifying events, decisions, or actions based on a set of beliefs or ideological principles.

Critical Thinker

A person who actively questions assumptions, evaluates evidence, and assesses conclusions logically.

Ideological Beliefs

Strongly held systems of ideas and ideals, especially those that form the basis of economic or political theories and policies.

Metaphysical

Metaphysical pertains to the branch of philosophy that explores the nature of reality, including concepts such as existence, the universe, consciousness, and beyond.