Find the area of the surface generated by revolving the curve xequalsStartFraction e Superscript y Baseline plus e Superscript negative y Over 2 EndFraction in the interval 0 less than or equals y less than or equals ln 5 about the y-axis.

The area is given by the integral,

We have

So now compute the integral:

Substitute and :

Another substitution, and :

There's a well-known formula for the integral of secant cubed, but if you don't know it off the top of your head (like me), you can integrate by parts:

Expand the remaining the integral in terms of powers of secant:

so that

Coming back to the area integral, we use the formula above to get

Next,

so the area is

step-by-step explanation:

abc