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 $2 \pi \int _ { a } ^ { b } g ( u ) \sqrt { \left[ g ^ { \prime } ( u ) \right] ^ { 2 } + \left[ f ^ { \prime } ( u ) \right] ^ { 2 } } \mathrm { du }$

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Definitions:

Fixed Costs

Business expenses that remain constant regardless of production volume, such as rent or salaries.

Total Overhead Variance

The difference between the actual overhead costs incurred and the standard or budgeted overhead costs anticipated for a particular period.

Direct Labor Hours

The total hours worked by employees directly involved in the manufacturing process or providing a service.

Manufacturing Overhead

Costs incurred in the manufacture of a product which are not directly traceable to specific units produced, such as utility costs and maintenance expenses.