Area of Surface of Revolution of ln(sec x) 0< x <(pi/6) W/A is no help here

[MrJones]

I tried doing just the integration and I was totally stumped, and Wolfram-Alpha has been no help at all

Find the surface area obtained by rotating about the x-axis:

ln(sec x) for 0 < x < (pi/6)

This problem appeared on an exam I had, but all that was required was to set up the integral but not solve for it. When I asked why we didn't have to solve for that particular problem, I was told it was too difficult for the amount of time given for the exam.

I have been trying to solve it and initially started by using (1/cos x) to solve, but it was not helpful so far.

Anyone? I appreciate any help!

Mr J

 

[Mark44]

I tried doing just the integration and I was totally stumped, and Wolfram-Alpha has been no help at all

Find the surface area obtained by rotating about the x-axis:

ln(sec x) for 0 < x < (pi/6)

This problem appeared on an exam I had, but all that was required was to set up the integral but not solve for it. When I asked why we didn't have to solve for that particular problem, I was told it was too difficult for the amount of time given for the exam.

I have been trying to solve it and initially started by using (1/cos x) to solve, but it was not helpful so far.

Did you sketch a graph of the curve being rotated? If you have that, it's pretty easy to set up an integral that represents the volume of the solid formed by rotation. Using disks, what is the volume of the typical volume element?

 

[D H]

This problem appeared on an exam I had, but all that was required was to set up the integral but not solve for it.

So what was your response on the exam -- how did you set up the integral?