Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 42

The formula provided represents the volume of the solid obtained by rotating the region enclosed by the curves y = 1 + cosx, y = 1, x = 0, x = pi/2 , about y axis, using washer method:
V = pi*int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)
You need to find the endpoints by solving the equation:
1 + cosx = 1 => cos x = 0 => x=-pi/2, x = pi/2
V = pi*int_0^(pi/2) (1 + cosx )^2 - 1^2)dx
V = pi*int_0^(pi/2) (1 + 2cos x + cos^2 x - 1)dx
V = pi*int_0^(pi/2) (2cos x + cos^2 x)dx
V = pi*(int_0^(pi/2) (2cos x) dx + int_0^(pi/2) (cos^2 x)dx)
V = pi*(2 sin x + int_0^(pi/2) (1+cos 2x)/2 dx)
V = pi*(2 sin x + x/2 + (sin2x)/4)|_0^(pi/2)
V = pi*(2sin(pi/2) + pi/4 + 0 - 2*0 - 0/2 - 0/4)
V = pi*(2 + pi/4)
V = (pi*(8+pi))/4
Hence, evaluating the volume of the solid obtained by rotating the region enclosed by the curves y = 1 + cosx, y = 1, x = 0, x = pi/2, about y axis, using washer method, yields V = (pi*(8+pi))/4.