Hello, I'm stuck as how to the find volume of the solid generated by revolving the region created by y = x cos x; y = 0; x = 0; x =pi/2 about the y-axis? Your help is much appreciated!

First is to set up the integral. I suggest using the cylinder approach - for each value of x you have a cylinder of radius x, height y, and width dx. The volume of that cylinder is

dV = 2 \pi x y dx

and the integral is then:

\int dV = \int _0 ^{\pi/2} 2 \pi x y dx = \int _0 ^{\pi/2} 2 \pi x^2 \cos x dx

Thank you so much!!