Homework Help: Finding Volume with Integration

1. The problem statement, all variables and given/known data
How do you determine what formula to use in a given volume question? I always confused about it. Like, when to apply shell, when should use washer, etc.

For example:
Find the volume of the solid generated by revolving the area between the curve y=(cos x)/x and the x-axis for π/6≤x≤π/2 about the y-axis.


2. Relevant equations
Should I use this one
[itex]V = \int\limits_{a}^{b}2\pi xf(x)dx[/itex]
Or this one
[itex]V=π\int\limits_{a}^{b}y^2dx[/itex]




3. The attempt at a solution
Using first equation, I will get
[itex]V = \int\limits_{\pi/6}^{\pi/2} 2\pi x \frac{cosx}{x}dx = 2\pi \int\limits_{\pi/6}^{\pi/2}cosxdx = 2\pi [sinx]_{\pi/6}^{\pi/2} = 2 \pi (1 - 1/2)= \pi[/itex]

I don't know how to calculate the second one but someone write the answer as follow
[itex]\pi \int\limits_{\pi/6}^{\pi/2}(\cos x/x)^2dx= \pi (-x) \frac{(-x Si(2x)+\cos^2(x))}{(x)}|_\frac{\pi}{6}^\frac{\pi}{2}=Si(\frac{\pi}{3})-Si(\pi)+\frac{9}{2\pi}[/itex]


Those answers are not equal. I have checked with wolframalpha.