Find the volume of the solid

Question

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the graphs of y=sinx/x , x=pi/2 , and the x~axis about the y~axis.

Answer 1

Since there won't be any closed form for the radius of a disk slice, we can't use the disk method.

 

So we must use cylindrical shells

 

The volume of the shell is

 

dV = 2π x sin(x)/x dx = 2π sin x dx

 

So the volume is

 

∫_V dV = 2π ∫₀^π/2 sin x dx = 2π[-cos x]₀^π/2 = 2π[-cos π/2 + cos 0] = 2π[0 + 1] = 2π