Chapter 8, Problem 51RE

To determine

To find : the area of the surface.

Answer to Problem 51RE

The area of the surface is $3.839$ .

Explanation of Solution

Given information : the curve about the x-axis $y=\tan x,0\le x\le \raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ .

Calculation :

The area of the surface is:

  $\begin{array}{l}A={\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{\int }}2\pi \cdot \tan x\cdot \sqrt{1+{\left(\frac{d}{dx}\tan x\right)}^2}}dx\\ A=3.839\end{array}$