R is bounded below by the x-axis and above by the curve?

Question

y=2cosx, 0≤ x ≤ pi/2. find the volume of the solid generated by revolving R around the y-axis by method of cylindrical shells

Answer 1

Using cylindrical shells find the volume V.
Integrate over the interval [0,π/2]

V = ∫2πxy dx = ∫2πx(2cos x) dx = 4π∫x(cos x) dx
= 4π(cos x + xsin x) = 4π{0 + (π/2)(1)} - 4π(1 + 0)
= 4π(π/2 - 1) = 2π(π - 2)