Set Up an Integral for the Area of the Surface $y = \cot x , 0 \leq x \leq \pi / 4 ; x$

question 214

Multiple Choice

Set up an integral for the area of the surface generated by revolving the given curve about the indicated axis.
- $y = \cot x , 0 \leq x \leq \pi / 4 ; x$ -axis

• A) \(\int _ { 0 } ^ { \pi / 4 } \csc x \sqrt { 1 + \cot x } d x\)
• B) \(\int _ { 0 } ^ { \pi / 4 } \cot x \sqrt { 1 + \csc ^ { 4 } x } d x\)
• C) \(2 \pi \int _ { 0 } ^ { \pi / 4 } \cot x \sqrt { 1 + \csc ^ { 4 } x } d x\)
• D) \(2 \pi \int _ { 0 } ^ { \pi / 4 } \csc x \sqrt { 1 + \cot x } d x\)

---

Definitions:

OH

Sometimes refers to the hydroxyl group, a functional group consisting of an oxygen atom covalently bonded to a hydrogen atom.

Denature

The process by which a protein's structure is altered, losing its biological function, typically due to factors like changes in pH, temperature, or exposure to chemicals.

Body Temperature

The measure of the body's ability to generate and get rid of heat, reflecting how well the body is functioning.

Fever

A temporary increase in body temperature, often due to an infection.