1. Sketch the graph of the function \(f(x) = \ln(\cos(x)),\) and consider the segment of this graph between the points \((0,f(0))\) and \((\pi/3,f(\pi/3))\).
   1. Calculate the arclength of this segment.
   2. Consider the surface that results from revolving this segment about the \(y\)-axis. Sketch this surface. Write down an integral that expresses the area of this surface. Play with this integral until you suspect, as I suspect, that evaluating it by hand is very difficult.
   3. Consider the surface that results from revolving this segment about the \(x\)-axis. Sketch this surface. Write down an integral that expresses the area of this surface.
   4. Based on your sketches, which of these two surface areas will be larger?
   5. Demonstrate how to evaluate the integral expressing the latter surface area.