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

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) $2 \pi \int _ { 0 } ^ { \pi / 4 } \csc x \sqrt { 1 + \cot x } d x$