Chapter 8.3, Problem 58E

To determine

To find : the area of the surface.

Answer to Problem 58E

The area of the surface is $2.999$ .

Explanation of Solution

Given information : The curve about the y-axis $x=\sqrt{2y-1},\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$8$}\right.\le y\le 1$ .

Calculation :

Let $g\left(y\right)=\sqrt{2y-1}$

Then, the surface area is given by:

  $\begin{array}{l}S=2\pi {\displaystyle \underset{c}{\overset{d}{\int }}f\left(y\right)\sqrt{1+f\text{'}{\left(y\right)}^2}\times dy}\\ S=2\pi {\displaystyle \underset{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$8$}\right.}{\overset{1}{\int }}\sqrt{2y-1}{\sqrt{1+f\text{'}\left(y\right)}}^{2}dy}\\ S\approx 2.999\end{array}$